Krishna's B.Sc. Physics Practical-IV | Edition-1F | Pages-45 | Code-1430

Table of contents :
B.Sc. Physics Practical-IV (Kumaun)
Dedication
Preface
Syllabus
Brief Contents
Exp. No. 1: To locate the positions of cardinal points
Exp. No. 2: Verify Newton’s formula and hence find the focal
Exp. No. 3: To determine the limit of resolution of a telescope
Exp. No. 4: To determine the resolving power of prism
Exp. No. 5: To verify Stefan’s law
Exp. No. 6: To find high temperature coefficient of resistance
Exp. No. 7: To study of random events or laws of probability distribution
Exp. No. 8: To verify the cauchy’s dispersion formula
Exp.No. 9: To determine the thickness of mica sheet by using Biprism

Citation preview

Krishna's

B.Sc. PHYSICS PRACTICAL-IV (For B.Sc. IVth semester students) As per Kumaun University Latest Semester Syllabus w.e.f. 2017-18

By

Avinash Sharma M.Sc., P.hD. Head, Department of Physics J.L.P.G. College, Hasanpur Amroha (U.P.)

Ashok Kumar M.Sc., N.E.T. Assistant Professor J.L.P.G. College, Hasanpur Amroha (U.P.)

, KRISHNA HOUSE, 11, Shivaji Road, Meerut-250 001 (U.P.), India

Jai Shri Radhey Shyam

Dedicated to

Lord

Krishna Author & Publishers

Preface

W

e are happy to present this book entitled “B.Sc. Physics Practical-IV”. It

has been written according to the Kumaun University Latest Syllabus to fulfil the requirement of B.Sc. IVth semester students.

The book is written with following special features: 1.

It is written in a simple language so that all the students may understand it easily.

2.

It has an extensive and intensive coverage of all topics.

3.

Sufficient viva-voce questions are added in this book. We are extremely grateful to our respected and beloved Parents whose

incessant inspiration guided us to accomplish this work. We also express gratitude to our family for their moral support. We are immensely thankful to Mr. S.K. Rastogi (Managing Director), Mr. Sugam Rastogi (Executive Director), Mrs. Kanupriya Rastogi (Director) and entire team of Krishna Prakashan Media (P) Ltd., for taking keen interest in this project and outstanding Management in getting the book published. The originality of the ideas is not claimed and criticism and suggestions are invited from the Students, Teaching community and other Readers.

–Authors

(vi)

Some Tips for Mixture Analysis

1

Syllabus B.Sc. PHYSICS PRACTICAL-IV B.Sc. IVth Semester Kumaun University (w.e.f. 2017-2018) List of Expt. for B.Sc. II year, semester IV (at least eight experiments which cover understanding of theory course)

Practical 1.

Nodal slide assembly, Location of cardinal points of lens system

2.

Newton ’s formula

3.

Dispersive power of prism.

4.

Limit of resolution of a telescope.

5.

To determine the Resolving Power of a Prism

6.

Stefan ’s law.

7.

Platinum resistance thermometer.

8.

J-Callendar and Barne ’s method.

9.

Random events- Statistical board method.

10.

Newton ’s law of cooling - Sp. heat of kerocene oil.

11.

To verify the Cauchy ’s dispersion formula.

12.

To find the thickness of the wire using optical bench.

13.

To determine the thickness of mica-sheet by using Biprism.

14.

To determine the Critical temperature and critical pressure of a gas.

15.

To measure temperature with the help of Jolly’s constant volume air thermometer.

(vii)

Some Tips for Mixture Analysis

1

Brief Contents Preface......................................................................................................................(vi) Syllabus....................................................................................................................(vii) Brief Contents..........................................................................................................(viii)

Exp. No. 1:

To locate the positions of cardinal points of a coaxial optical system of two thin convergent lenses separated by a distance with the help of nodal slide and verify the formula......................................................(01-07)

Exp. No. 2:

Verify Newton’s formula and hence find the focal length of a given convex lens........................................................(07-10)

Exp. No. 3:

To determine the limit of resolution of a telescope...........(10-14)

Exp. No. 4:

To determine the resolving power of prism......................(15-18)

Exp. No. 5:

To verify Stefan’s law.......................................................(18-23)

Exp. No. 6:

To find high temperature coefficient of resistance of platinum using a (Platinum resistance thermometer)...........(23-28)

Exp. No. 7:

To study of random events or laws of probability distribution......................................................................(28-33)

Exp. No. 8:

To verify the cauchy’s dispersion formula..........................(33-37)

Exp.No. 9:

To determine the thickness of mica sheet by using Biprism............................................................................(37-40)

(viii)

Experiment No -1 Object : To locate the positions of cardinal points of a coaxial optical system of two thin convergent lenses separated by a distance with the help of nodal slide and verify the formula

and

L1H 1 =

+ xF f2

L2H 2 =

− xF f1

Where F is the focal length of the coaxial optical system of two thin convex lenses of focal lengths f1 and f 2 when they are separated by a distance x. Apparatus used : Nodal slide assembly, a bulb in a metallic container, cross slit screen, nodal slit and plane mirror and two thin convex lenses of nearly same and of short focal length. Cardinal points and formula used : In optical system has four cardinal points (i) Two principal points (H 1, H 2) or nodal points ( N1, N 2) and (ii) two focal points (F1, F2). (1)

The distance of the Ist principal point H 1 from the first lens L1 is given by L1H 1 =

(2)

xF f2

The distance of IInd principal point H 2 from the second lens L2 is given by L2H 2 =

− xF f1

2 Method : 1. Make all the adjustments in the apparatus and measure the focal length f1 and f 2 of the two convergent lenses separately in similar manner. 2. Mount the two convex lenses on the lens holders of the nodal slide such as the lens L1 is towards the plane mirror and lens L2 forces the cross-slit as shown fig. 3. Measure the focal length of the combination of lenses. When the position of nodal slide carriage and nodal slide up right are adjusted for number lateral shift, the cross slit screen lies in the second focal and the nodal slide upright represents the second nodal plane of the lens L2 and principal point H 2 or axis of rotation is H 2L2. Note this distance between the nodal slide up right (or axis of rotation of nodal slide) and cross slit upright are recorded from their index marks on the optical bench. This is equal to the focal length F of the combination. By convention L2H 2 is five as lies left to the lens L2. Also note the distance H 1F1, that is focal length of combination of two lenses when separated by distance x. 4. Calculate the bench correction and repeat the procedure. Observations : 1. Length of glass rod, y = .... cm 2.

Observed distance between the cross-slits and nodal slide upright, x = − cm

3.

Bench correction = y − x = ± .... cm x +

H2

F2

L2H2 F

N2 Carriage L1

L2 Axis of rotation

Linear scale Optical bench Fig. 1 : Nodal slide assembly (Optical bench)

One face of lens other face of the lens One face of the lens other face of the lens One face of the lens other face of the lens

1.

2.

3.

—

—

—

—

—

—

Light Position of Position of incident on cross slit upright (b) up right (a) cm cm

—

—

—

Observed focal length f1 ( a − b) cm

For Lens L1 Corrected focal length f1 (cm)

Mean focal Position of Position of Observed length f1 cross slit lens up focal (cm) up right ( a′ ) right ( b′ ) length f 2 cm cm ( a ′ − b′ ) cm

For Lens L2 Corrected focal length f 2 cm

Mean focal legnth f 2 (cm)

Table 1 : For the measurement of focal lengths of two lenses ( f1 , f 2 )

(a)

S.No.

Now rotate the nodal slide carriage through 180° so that the position of lenses L1 and L2 interchanged. In this stage lens L1 faces the cross slit and L2 is towards the plane mirror. Again obtain the position of number of lateral shift of the image as described above. Note the distance of the Ist principal point H 1 from the Ist lens L1 by recording the readings of their respective uprights.

4.

3

—

—

—

—

1.

2.

3.

1.

2.

L1

3.

—

S.No.

L2

Position of cross slit ( a ) cm

—

—

—

—

—

Position of axis of rotation of nodal slide ( b) cm

—

—

—

—

Focal length of combination F ( a − b) cm

Separation between the two lenses x = ..... cm

—

—

H1 F1 =.... cm

—

—

H 2 F2 =.... cm

Mean F (cm)

—

—

—

—

—

—

Position of the axis of rotation of nodal slide or principal point on the linear scale attached to the carriage H (cm)

—

—

—

—

—

—

Distance between lens towards cross-slit and axis of rotation of nodal slide (cm)

L1 H1 = ..... cm

L2 H 2 = ..... cm

Mean distance (cm) practical value

Table 2 : For the measurement of focal length F of the combination and distance L1 H1 and L 2 H 2

Lens towards cross slit

(b)

4

B.Sc. Physics Practical-IV

5 Calculations : 1. The mean focal length of the combination of two coaxial thin convex lenses 2.

F = … cm The theoretical value of L1H 1 as obtained by the relation, L1H 1 =

3.

xF = + … cm f2

The theoretical value of L2H 2 as obtained by the relation L2H 2 =

− xF = … cm f1

Result : 1. The calculated and experimentally determined value of L1H 1 and L2H 2 are approximately same and hence the formula L1H 1 = 2.

xF f2

and L2H 2 =

− xF are verified. f1

Location of cardinal points To locate the cardinal points, sketch the two thin converging lenses L1 and L2 at known distance x = …cm apart. Mark the positions of Ist and IInd nodal point H 1 and H 2 at a distances L1H 1 = ... cm from lens L1 and L2H 2 = … cm from lens L2 on the common principal axis of the two lenses with proper sign. As the medium on both sides of the lenses are air the principal point coincides with the nodal points, therefore, mark N1 and N 2 on H 1 and H 2 respectively. Measure the distance H 1F1 from H 1 and H 2F2 from H 2 and locate focal points F1 and F2 with proper sign. x = cm H2L2= ...cm H2 N2

F1

H1L1 = ...cm L1

H1 N1

F2

F2 = cm L2

Fig. 2 : Location of nodal point

Precautions and sources of error : 1. The mirror used in the experiment should be truly plane. 2. Bench error should be properly accounted for.

6 3. 4. 5.

All the uprights arranged on the optical bench should be adjusted to the same height. The cross slits must be properly and intensely illuminated. For searching nodal point on the principal axis of the lens system or lens, the rotation of the nodal slide about the vertical axis should not exceeded by 5° or so.

Viva-Voce Q.1.

What is nodal slide ?

Ans.

Nodal slide is a small horizontal metal carriage having two lens holders. The separation between the lens placed in the lens holders can be changed and directly read on the linear scale provided with the carriage. The metal carriage as a whole can be moved back and forth in horizontal direction as well as can be rotated about a vertical axis.

Q.2.

Why do you call it nodal slide ?

Ans.

It is so called because it is used to locate the nodal points of a lens system.

Q.3.

What is angular magnification ?

Ans.

If the incident ray and conjugate emergent ray make angle θ1 and θ2 with principal  tan θ2  axis, then the ratio of tangent of θ2 and θ1 ,   is called the angular  tan θ1  magnification of the lens.

Q.4.

Do you know any other pairs of such points ?

Ans.

Yes, there are two other pair of points of an optical system, called focal points and principal points.

Q.5.

What is the common name of these three pairs of points of the coaxial optical system ?

Ans.

The common name of all these points of a coaxial system is called cardinal points.

Q.6.

Who discovered the nodal points ?

Ans.

The nodal points were discovered by listing.

Q.7.

What is longitudinal magnification ?

Ans.

The ratio of extension of the image to the extension of the object along the principal axis is called the longitudinal magnification of the lens system.

Q.8.

What is the focal length of a combination of two coaxial thin lenses of focal length f1 and f 2 when they are separated by a distance x?

Ans.

The focal length f of the combination of two thin lenses of focal lengths f1 and f2 when they are separated by a distance x is given by 1 1 1 x = + − f f1 f2 f1 f2

7 Q.9.

When they are in contact ?

Ans.

When two lenses are in contact, the combined focal length F is given by 1 1 1 = + F f1 f2

Experiment No-2 Object : Verify Newton’s formula and hence find the focal length of a given convex lens. Apparatus used : Optical bench (≈ 2 m long) with two needless and three uprights, a lens holder, upright, a convex lens and a plane mirror with a stand. Formula used : B

x2

(P) A

O x1

A' F2

F1

(Q)

B' Fig. 3

Let F1 and F2 the two principal focii of the lens and x 1 = Distance of object needle from first principal focus x 2 = Distance of image needle from 2nd principal focus of the lens then focal length of the lens, f = x 1x 2 Theory : Let the real image of the object AB be formed at A1B1 by a lens of focal length f then u = − ( f + x 1), v = ( f + x 2) 1 1 1 = − f v u or

1 1 1 = + f f + x 2 f + x1

8 1 2 f + x1 + x 2 = f ( f + x 2) + ( f + x 1)

or ∴

2 f 2 + fx 1 + fx 2 = f 2 + fx 1 + fx 2 + x 1x 2

∴

f = x 1x 2

Procedure : 1. Find rough focal length of the lens by focussing the rays of light from a distant object on screen to get a well defined sharp image on the screen and measure the distance of lens from the screen. 2. To find the position of focal points.

P

O

O

F1

Q

F2 (b)

(a) Fig. 4

3.

4.

5.

6.

Place a plane mirror vertically to the right of the lens with the plane face towards the lens fixed on the upright. Make the tip of needle P coincide with the tip of its image and remove the parallax between the needle and its image. Note the position of this needle (P). It gives the position of Ist focal point F1 fig 4 (a). Now place the mirror to the left of the lense without distrubing the position of the lens and again remove the parallax between needle Q and its image. Note the position of needle (Q). If gives the position of 2nd focal point F2. fig 4 (b). Without disturbing the lens, place the needles P and Q beyound F1 and F2 as shown in fig. and remove the parallax between the needle Q and the image of P or between the needle P and image of Q. Find distance of needle P from F1 this gives x 1 also find the distance of needle Q from F2 and gives x 2. Repeat the above observation by changing positions of needle P and finding the corresponding positions of needle Q after removing parallax.

Observations : Rough focal length of the lens = … cm

9 Position of Ist focal point, F1 = ... cm Position of IInd focal point, F2 = ... cm Position of lens (not to be changed throughout the experiment) = … cm S.No.

Position of x 1 = F1 ⋅ P object OA − OF1 needle ( P)

Positions x 2 = F2 A − F = x 1 x 2 of image OA ′ − OF2 x 2 x 1 cm needle ( Q)

1.

—

—

—

—

—

2.

—

—

—

—

—

3.

—

—

—

—

—

4.

—

—

—

—

—

Mean value of f = x 1x 2 = ... cm from the table, it is clean that values of x 1x 2 are constant within experiment error hence Newton’s formula is verified. Result : Mean f = x 1x 2 = ... cm Precautions : 1. First join the image of tip of needle P and tip of needle Q and then remove the parallax of needle Q and image of needle P or needle P and image of needle Q. 2. Do not change the stands of the needles or lens. 3. Don’t disturb the position of the lens, once its position has been noted. 4. Don’t interchange the positions of uprights during the experiment.

Viva-Voce Q.1.

What is lens ?

Ans.

A lens is a piece of transparent medium (such as glass, plastic or some liquid) bounded by two surfaces and at least one of the surface is spherical.

Q.2.

What is real image in a lens ?

Ans.

When the rays of light after refraction from the lens actual meet at the image then the image formed is said to be real. A real image can be obtained on a screen.

Q.3.

What is focal length ?

Ans.

It is the distance of principal focus of the lens from its optical centre.

Q.4.

What is optical centre of thin lens ?

Ans.

For a thin lens, optical centre is a point through which a light ray passes undeviated.

10 Q.5.

What is lens maker’s formula ?

Ans.

 1 1 1  = (µ − 1) −  f  R1 R2  Where R1 and R2 are radii of two spherical surfaces of lens and µ is refractive index of the material of lens.

Q.6.

What is 1-Diopter ?

Ans.

Power of a lens is 1-Diopter if its focal length is one meter.

Q.7.

Write the formula of power of a lens. 1 P= f(in meter)

Ans.

where f is the focal length of lens. Q.8.

What is parallax ?

Ans.

If the apparent shift between two objects, or between an object and an image situated at different distances from the eye, when eye is removed to and fro.

Q.9.

What is Gaussian form of lens equation ? 1 1 1 = − f v u

Ans. Q.10.

Can you even have a real image through a convex lens ?

Ans.

Yes, if the rays falling on the concave lens are convergent.

Experiment No-3 Object : To determine the limit of resolution of a telescope. Apparatus used : A telescope fitted with a rectangular adjustable slit. A black card board with narrow white strips on it (or black painted glass plate with two fine parallel slits about 2 or 3 mm apart), travelling microscope and a measuring tape (or meter scale), a source of light (sodium lamp). Theory : The resolving power of a telescope represents its ability to form separate and distinguishable images of two distant objects kept close to each other. It is measured by the angle subtended at objective of the telescope by two objects which are just resolved by it. The smaller the value of this angle, the high is the resolving power of the telescope. This angle is a measure of the limit of resolution of the telescope which can be defined as the smallest angle subtended at the objective of the telescope by the two objects, which are just resolved by the telescope. For a telescope fitted with a rectangular aperture, the limiting angle of resolution θ, is given by

11 θ=

d λ = D a

Procedure : 1. Mount the black painted glass plate (or metal plate) carrying two fine parallel slits on a stand such that its plane is vertical. Illuminate the slits (objects) by a source of light placed behind them. (If such a glass plate is not available then take a glass sheet and cover it with a thick black paper. Using a razor blade, draw two narrow and straight slits at a distance of about 2-3 mm from each other. 2. Mount the telescope on another stand at the same height of glass plate such that its axis is horizontal and normal to the glass plate. Now clamp the rectangular aperture of adjustable width on the objective of the telescope in such a way that its axis becomes parallel to slits (i. e. vertical). 3. Plate both the stands at suitable distance (about 5 or 6 fit). Now open the aperture slit) fully with the help of micrometer screw. More the telescope in the horizontal direction with its rack and pinion arrangement such that the images of the object slits are distinctly visible and lie symmetrically w.r.t the intersection of the cross wire in the field of view of the eye piece. If necessary, also adjust the height of telescope. 4. Gradually reduce the width of aperture (slit) of telescope objective by micrometer screw till the two line images of the object slits just cases to appear as two (just separate). In this position, if you reduce the width of slit; a stage comes where the two line images are resolved i. e. by reducing the aperture just a little of two images blend together to form a single image. Stop at this stage of just resolution. Note down the reading of micrometer. 5. Now, close the aperture (slit) completely by moving the micrometer screw (till the brightness of the images dust disappearis). Note down the micrometer reading also. Take the difference of these two readings which gives the width of aperture (slit) just sufficient to resolve the two images (If micrometer arrangement is not provided with the aperture slit), then the aperture is gradually reduced till the two images. If cease to appear two. Take out the rectangular aperture (slit) and measure its width with the help of two travelling microscope. 6. Measure the separation between the pair of object slits with the help of a travelling microscope which gives ‘d ’. 7. Also measure the distance (D) between the glass plate having object slits and the aperture (slit) of the telescope objective. 8. Repeat the experiment for 4 or 5 times for different values of D. (The different observations can also be taken by taking different object slits).

12 Lamp Rectangular object

Telescope

Slit

Micro meter screw

To mains (Rectilinear object slits)

Stand Fig. 5 : Telescope system

Observations and Calculations : 1. Mean wavelength of light used : λ = 6000 × 10−8 cm (or Mean wavelength of sodium light used) λ = 5893 × 10−8 cm 2.

Table for width (a) of rectangular aperture (slit) when micrometer arrangement is used : Least count of the micrometer screw = … cm Table 1

Distance Reading of Micrometer screw of the When images of slits When aperture (slit) is slits cease (just resolved) closed plate S.No. from the M.S V.S. M.S. Total Total V.S. telescope reading reading reading reading x-cm m y-cm objective m v v D'cm

Theoret -ical width of reasonrectaning gular power apera λ   ture  a a=x−y

1.

—

—

—

—

—

—

—

—

—

2.

—

—

—

—

—

—

—

—

—

3.

—

—

—

—

—

—

—

—

—

4.

—

—

—

—

—

—

—

—

—

13 V.S reading, v = vernier scale reading h.c of micrometer Table for width the aperture (slit) when microscope is used Least count of the microscope = …… cm Table 2 Reading of the microscope when crosswire coincides with Distance S.No. D cm

One end of the (Slit) M.S

V.S

Total x-cm

Other end of the slit M.S.

V.S

Total y-cm

Width a = x − y

1.

—

—

—

—

—

—

—

—

2.

—

—

—

—

—

—

—

—

3.

—

—

—

—

—

—

—

—

Table for the separation (distance) between two object slits (d) Least count of the travelling microscope = … cm Table 3 Microscope reading

S.No.

Position of Ist image (one end) M.S

V.S

Total x-cm

1.

—

—

—

2.

—

—

—

3.

—

—

—

Position of IInd image (other end) M.S.

V.S

Total y-cm

Distance between the two object slits d= Y −X

Distance of the object slits from the telescope objective D cm

Practical resolving,  d power    D

Generally, the distance between the two object slits, d = 2 mm (or 3 mm) Result : 1. The theoretical and practical resolving powers (limit of resolutions) of the telescope are shown in the table : Distance of object slits from S.No. the telescope objective D cm 1. 2. 3.

Theoretical resolving power λ    a

Practical resolving power  d    D

14 2.

Resolving limit =

1 = … (Theoretical) = … (Practical) (Resolving power)

Precautions and Sources of Errors : 1. The plane of two parallel slits on the plate should be vertical and parallel with the rectangular aperture. 2. The axis of telescope should be horizontal. 3. Back less error in the micrometer screw should be avoided. 4. The width ‘a’ of the rectangular aperture should be measured very carefully. 5. The distance ‘D’ between the plate of object slits and rectangular aperture should be measured accurately.

Viva-Voce Q.1.

What do you mean by the resolving power of a telescope ?

Ans.

The resolving power of telescope is its capacity to make two close distant objects to appear as separate and distinguishable from each other.

Q.2.

On what factors does the resolving power of a telescope depends ?

Ans.

The resolving power of a telescope is given by dθ = λ / a. Hence, resolving power is directly proportional to λ, the wavelength of light used and inversely proportional to the width of slit (a).

Q.3.

How will you define the resolving power of a optical instrument ?

Ans.

The ability of an optical instrument to produce separate and distinguishable image of two objects, which are very close to each other, is called its resolving power.

Q.4.

What do you understand by just resolved ?

Ans.

The limit of closeness of two objects into which they can be seen separate.

Q.5.

When does the resolution of two images possible ?

Ans.

When the centre of one may, at the most lie on the edge of the other. If the images come closer than this then, they cannot be resolved and will give the sensation of one image only. This criterion has been furnished by Lord Rayleigh.

Q.6.

What is the resolving power of a normal eye ?

Ans.

The resolving power of a normal eye is about one minute.

Q.7.

What is the use of employing objectives of large focal lengths ?

Ans.

A large focal length of the objective result the large magnifying power of the telescope.

15

Experiment No-4 F

Resolving Power of Prism

Object : To determine the resolving power of prism. Apparatus used : Spectrometer, prism, etc. Formula used : Resolving power is given as λ  dµ  −2Bt = t  = 3  dλ  dλ λ Slit to resolve a close doublet (α1 − λ 2) = dλ t is related to w by given equation A ( A + D) t = 2w sec  sin  2  2  Where A is the angle of prism which is usually 60° and D is the mode of angle of deviations for wavelengths λ 1 and λ 2. Thus

λ 4 Bw A ( A + 1) = − 2 ⋅ sec  sin  dλ 2 λ  2 

…(1)

Experimental Setup and Procedure : Set up the spectrometer as shown in figure measure the prism angle A and record it. Now measure the value of B and record it. Again record the angles of minimum deviation for D1 and D 2 lines (λ 1 = 5896 Å and λ 2 = 5890 Å) Now calculate average wavelength of λ 1 and λ 2, λ=

λ1 + λ 2 2

and record it which is nearly 5.893 × 10−5 cm. Now take a procedure to record w

16 Prism Collimator lens Light source

Prism table

Collimator

Verni e

r

Crosswire Eyeblue Fig. 6

Mount a variable slit fitted with micrometer screw on the objective of telescope. Record its least count make it error free. Illuminate the collimator slit with monochromatic light source (sodium lamp) and form its spectrum. Two orange-yellow lines are seen clearly. Now close the slit gradually and set it at a position such that D1, D 2 lines just cease to appear separate. Note the width of the slit w in cm. Repeat this experiment to calculate the average value of w. Now calculate

λ by putting λ = 5.893 × 10−5 cm and dλ = 0.006 × 10−5 cm dλ

and put the value of B, w, λ , A and D in equation number 1 and calculate its value. The numerical values of two sides must be close to each other, record all observations, specifications and findings in suitable form in table. Observations : 1. 2. 3.

Value of M. S. division in ° C or ′ or ′ ′ Number of vernier divisions Specifications of prism material …… Specifications of light sources used …… Least count of spectrometer =

C.S.

... ...

M.S.

...

...

With closed

...

...

TRW

...

...

MS

...

...

CS

For resolution dλ

Micrometer reading for slit width

Table for resolving power.

Observation :

...

...

TR(b)

Angle of prism A

Angle of Min. dev. for λ Mean ‘λ’

Difference Cauchy dλ constant β

λ / dλ

R.H.S. of equations

17

18 Precautions : 1. Use spectrometer carefully. 2. Spectrometer can be used once for a particular light. 3. Slit should be as narrow as possible.

Viva-Voce Q.1.

What is angle of minimum deviation ?

Ans.

The minimum value of angle of deviation for particular angle of incidence is called angle of deviation.

Q.2.

Is it necessary to place the prism in the position of minimum deviation ?

Ans.

Yes, because we obtain bright and distinct. Spectrum and magnification is unity at this condition.

Q.3.

What is the wavelength of sodium light ?

Ans.

λ1 = 5896 Å, λ 2 = 5890 Å

Q.4.

What is the wavelength difference of sodium D1 and D2 lines ?

Ans.

dλ = 6 Å

Q.5.

Which kind of eyepiece we use in physics lab ?

Ans.

Ramsdon’s eyepiece.

Q.6.

What are the main parts of spectrometer ?

Ans.

(i) Collimator (ii) Prism table (iii) Telescope

Q.7.

What is Cauchy equation ? B µ = A + 2 , where µ is the refractive index of the prism. λ

Ans.

Experiment No-5 Object : To verify Stefan’s law. Apparatus used : One 6 volt battery, one rheostat (100 Ω), one D.C. voltmeter (0-10 volt), one D.C ammeter (0-1 Amp) one tungsten filament electric bulb (6V, 6W). Stefan’s law, for a black body, is E = σ(T 4 − T04 ) Where E is the net amount of radiation emitted per second per unit area of a black body at temperature T (on kelvin scale) and surrounding by another body assumed black) at temperature T0 and σ is Stefan’s constant.

19 A similar relation can also hold for bodies that are not black. In such a case we can write P = λ (T α − T0α ) Where P is the total power emitted by a body at temperature T surrounded by another body at temperature T0, α is a power close to 4 and λ is some constant depending on the material and surface area of such a body. Further, the above relation can be put as  Tα P = λT α 1 − 0α  T   Now, it T >> T0 (e. g . T = 1500° K and T0 = 300 K) We can write ∴

P = λT α log P = α log T + log λ

This is similar to equation y = mx + c. Hence a graph between log P and log T should be a straight line whose slope gives α. If α comes out to be 4 (nearly) then Stefan’s law is verified. Therefore, in order to verify Stefan’s law, we have to evaluate different values of P (power radiated) and corresponding value of T (on kelvin scale). Here, the radiating body is the tungsten filament whose temperature t°C is given by Rt = 1 + αt + βt 2 R0 Where α and β are constant known for any material. Here Rt and R0 are the resistance of the filament at t°C and 0°C respectively. Method : 1. The electrical circuit is completed, as shown in fig 8. Two wires are soldered directly to the base point of the bulb, these are connected to the voltmeter to measure to voltage V across the filament. It is ensured that with help of the rheostat the current can be varied from a low value below glow stage of the filament of the bulb to such a high value that the filament becomes dazzling white. 2. The current is so adjusted that the filament just glows it happens when the temperature of the filament is 800°K. Servel trials with increasing and decreasing current (i. e. from below glow stage and beyound glow stage) are made. Everytime the values of voltage V and current I at just glow stage are noted. Ratio V/ I gives the resistance Rg of the filament at just

20 glow stage (i. e. at 800° K temperature of the filament). The mean value at 0°C or R273 (filament resistance at 273°K) is then obtained by the relation. R800 = 3.9 R273 or

∴ 3.

4.

Rg R273

From the given graph of

RT for tungsten, we find R273 T that 800 = 3.9 at 800°K R273 or

= 3.9

R273 =

Rt R0

Rg

3.9 This gives the tungsten filament resistance at 0°C or 275 K. i. e. R0 or R273. Now the filament current I is varried from a value below stage to values high enough to get dazzling while light. Each time the values of V and I are noted. From these the values of P = VI V and Rt or RT = are evaluated each time. I R R Knowing the value of R0 or R273 the ratio t or T is calculated. R0 R273 R RT Using the given t versus t or versus T graph, the filament R0 R273 temperature t°C or T °K is found out corresponding to each value of P. A graph is then plotted between log P (on Y-axis) and log T (on X-axis). A straight line obtained. By taking any two point A and B on this line, it’s slop is evaluated from the relation. Slope = tan θ =

BC AC

This comes out to be nearly 4. Y B

Log P A

O

θ

C

Log T Fig. 7

X

21 Battery

Rheostat

Filament

Bulb

Rh A Ammeter V Voltmeter Fig. 8 : Stefan’s law (electrical circuit)

Observation and Calculations : (A) Determination of filament resistance Rg at just glow state : Temperature of filament = 800°K Reading at just glow stage

S.No.

Current increasing Voltage V in volt

Current I (Amp)

Current decreasing Rg

V = Ω I

Voltage in volt

Current in Ampere

Rg =

V Ω i

1. 2. 3.

Mean value of Rg = ...... Ω Rg or R800 R273

= 3.9

(B)

S.No.

1. 2. 3. 4. 5.

Rg

= …… ohm. 3.9 Determination of power discipated P at different filament temperature : R273 =

Voltage V volt

Current I (Amp)

Power P = VI (watt)

logP

Resistance V RT = I

RT R 273

Temperature from Graph

logT

22 Result : The graph between log P and log T comes out to be a straight line. Hence P = λT α is verified further the slope of the line gives α = 4 and therefore Stefan’s fourth power law is verified. Precautions : 1. The resistance of filament Rg at just glowing temperature should be determined carefully. 2. The voltage applied across the filament should not exceed 6 volt. 3. The experiment should be performed in dark room so that just glowing stage of the filament may be correctly judged.

Viva-Voce Q.1.

What do you mean by Stefan’s law ?

Ans.

The total radiated energy per sec by a unit area of a perfect black body is directly proportional to the 4th power of the absolute temperature of the surface of the body, that is E ∝ T 4 or E = σT 4 , where σ is called Stefan’s constant.

Q.2.

What is the value of Stefan’s constant ?

Ans.

The value of Stefan’s constant σ is 5.67 × 10−5 erg/(sec-cm 2 -K 4 ) in C.G.S system and 5.667 × 10−8 Joule (sec-m 2 -K 4 ) or 5.67 × 10−8 Watt/m 2 -K 4 in S.I system.

Q.3.

What is a black body ?

Ans.

A body which absorbs all the incident radiation irrespective of frequency is called black body.

Q.4.

What is radiating body in your experiment ?

Ans.

Radiating body in our experiment is tungsten filament.

Q.5.

What is cathode ?

Ans.

A metal surface that act as an electron emitter is called cathode.

Q.6.

Define temperature coefficient of resistance ?

Ans.

The temperature coefficient of resistance is defined as the increase in resistance per unit length per degree rise in temperature.

Q.7.

What is an ammeter ?

Ans.

It is moving coil pivoted type galvanometer with a low resistance shunt across the coil of a galvanometer.

Q.8.

What is the importance of Stefan’s constant σ ?

Ans.

Stefan’s constant σ is used to determine the heavenly bodies like sun.

Q.9.

What is voltmeter ?

Ans.

It is also moving coil pivoted type galvanometer in which a high resistance is put in series with the coil.

23 Q.10.

What happens to the resistance if the temperature is raised ?

Ans.

Resistance increases with increases of temperature.

Experiment No-6 Object : To find high temperature coefficient of resistance of platinum using a (Platinum resistance thermometer). Apparatus used : Platinum resistance thermometer galvanometer, callender and Griffith bridge one way key, celsius thermometer. Theory : Platinum Resistance Thermometer Principal electrical resistance of a metallic platinum wire increases uniformly with rise in temperature. Platinum wire is wounded in the form of a double spiral on a mica strip inside a porcelain tube. Mica discuss with holes are provided inside the tube so that the lead wires do not touch each other. The free ends of the platinum wires are connected to terminals, marked Pρ using copper-lead wires. Two exactly similar Cu-Pb wires are connected to terminal CC. These are used to compensate the resistance of leads connected to platinum wire. The whole tube is sealed and terminals P, P, C, C are provided at the top. P P

CC

Mica discs

Compensating Cu leads

Mica sheet Pt wire Fig. 9 : Platinum resistance thermometer

24 R0, R1 and R2 be the resistance of Pt wire at temperature 0°C, t1 °C and t2 °C respectively then R2 = R0(1 + αt2) R1 = R0(1 + αt1) R2 1 + αt2 = R1 1 + αt1

∴

R1 + R1αt2 = R1 + R2αt1

∴ ∴

α[R1t2 − R2t1] = R2 − R1 α=

R2 − R1 R1t2 − R2t1

Callender and Griffth Bridge : It is a modified wheat stone bridge. The ratio arms P and Q are made equal. The platinum wire leads PP are connected in arms S. The compensating lead wires C1C 2 are connecting in arm R which contain variable resistance in the form of three variable coil resistances as shown in fig. 10 below. The arms R and S are connected through a wires (MN) of uniform thickness. The galvanometer is connected through a sliding contact with this wire MN.

P

P

C C x MO D

Mica disc

A

Por celair tube

N P1

C2 C1

P2

G

Q

P

Pt wire Mica strip

C

K1 Fig. 10

Make the connection as shown in fig. Press the key K1 and adjust the position of jockey on wire MN for zero deflection in the galvanometer. Let the balance point

25 be obtained at a distance x to the right from centre O of the wire MN of length 2l. So that MD = l + x and ND = l − x If Rt and S are resistances in R-arm and S-arm, and ρ be the resistance per unit length of wire MN, then at balance point. Rt + r + (l + x )ρ = S + r + (l − x )ρ R t = S − 2xρ Here r = resistance of the Cu leads in both arms Thus knowing S. x .ρ, one can fine Rt . (b)

To find ρ i. e., resistance per unit length of wire MN.

Short circuit both the gaps P1P2 and C1C 2 by using thick copper wires or thick Cu strips. Take out a small value of resistance R1 from arms R of the bridge and find the balance point. It will be to the left of central zero of MN, at a distance of from O. Then

R1 + (l − y) ρ = 0 + (l + y) ρ R1 = 2yρ or ρ =

R1 2y

Procedure : (a) To find the position of zero of wire MN. (1) Make the connection as shown in fig. (2) Short circuit P1 and P2 and C1 and C 2 with Cu strips or thick Cu-wires. Keep resistance in branch R to be zero. Find the position of null point by moving jockey over MN. Let it be at O. The O is the zero of wire MN. (b) To find ρ (resistance per unit length of wire MN). (1)

Keep P1 and P2 and C1 and C 2 short circuit. Take out of some low value of resistance r1 from branch R of the bridge. (1 – y)

(1 + y)

y O l

l Fig. 11

Let the null point be obtained at a length y to the left of O. Then r1 + (l − y)ρ = 0 + (l + y)ρ

26 ρ= (c) (1) (2) (3) (4)

(d)

r1 2y

To find resistance of platinum wire Rt and R100 at room temperature and at steam temperature. Remove Cu-strips from P1 and P2 and C1 and C 2. Connect terminal PP of platinum resistance thermometer in S bench in P1P2 gap and CC in R-bench in C1C 2 terminals. Insert key K1 and dip the porcelain tube of Pt. resistance thermometer in beaker containing water at room temperature. By touching the jockey at various points on MN, find balance condition. Let it be at a length ‘a’ to the right of O. Let resistance in arm-R be R. R + (l + a)ρ + r = R ± (l − a)ρ or Similarly find R100

Rtt = R + 2aρ

Observations and Calculations : 1. Electrical zero ‘0’ of the wire Mn = …… cm 2. To find ρ S.No

Resistance in branch R( r1 ohm)

Shift of balance point y from O y = …… cm

ρ=

r1 2y

1. 2. 3. 3.

Mean ρ = …… ohm/cm To find Rt Temperature of water bath t1 = …°C S.No

Resistance of R-branch

1. 2.

R1

3. 1. 2. 3.

R2

Shift of balance point a from O

Rt = R1 + 2aρ

27 Mean R1 = …… ohm Mean R2 = …… ohm Temperature of boiling water = t2 ∴

α=

R2 − R1 = ...... ° C−1 R1t2 − R2t1

Standard value of α = ...... ° C−1 Percentage error =

Satandard value − exp. value × 100 = .....% Standard value

Precautions : 1.

Thick copper strip or thick copper wires should be used to short circuit + P1P2 and C1C 2 gap.

2.

All connections should be tight.

3.

The ends of wire should be well cleaned by sand paper.

4.

Position of null points should be taken when the temperature of boiling water is constant.

Viva-Voce Q.1.

How does the resistance of Pt-wire change with increase of temperature ?

Ans.

It increases with the increases of temperature Rt = R0 (1 + αt + βt 2 ). At not very high temperature, βt 2 may be neglected, β being very small.

Q.2.

Why Pt-wire used for measuring temperature ?

Ans.

The resistance of Pt-wire increases appreciably and uniformly with the increase of temperature.

Q.3.

Define the temperature coefficient of resistance ?

Ans.

It is increase in resistance per unit length per degree rise in temperature.

Q.4.

What are the merits of Pt-thermometer ?

Ans.

1.

It has a wide range −200°C to 1200°C.

2.

The accuracy is high ≈ 0.01°C.

3.

It can be used to find the temperature of a furnace.

Q.5.

When is wheatstone bridge most sensitive ?

Ans.

When the resistance of all the ratio arms are of the same order.

Q.6.

Upto what range, can we use glass tube instead of porcelain tube ?

Ans.

Upto 700°C and beyond 700°C, glazed porcelain tube is used.

28 Q.7.

What is the principle of calender and Griffith’s bridge ?

Ans.

It is a modified version of wheat stone bridge.

Q.8.

What is the purpose of using compensating leads ?

Ans.

To compensating any change in the resistance of the leads connecting Pt-wire.

Q.9.

What is the principle of wheatstone bridge ? P R = Q S

Ans. Q.10.

What is the unit of resistance ?

Ans.

The unit of resistance is ohm (Ω).

Experiment No-7 F

Random Events-statistical Board Method

Object : To study of random events or laws of probability distribution. Apparatus used : Some identical coins (at least + 20 coins), plastic mug, statistical board (cylinderical card board), wooden tray (with boundary) or carrom board. Procedure : 1. First of all use wooden board. Make its base smooth and clean. 2.

Now put a coin in a given tumbler, shake it well and through it gently on the wooden board. Now noted how much head of coin is up, how much tail is up. Repeat this upto at least 100 times and record this result in table 1.

3.

Now take two coins and put them in a given tumbler as part (2). Now shake them well and throw on carrom board. Now note that how many times both have heads up, both have fails up and one has head up and other has tails up. Repeat this up to 100 times this is recorded in table 2.

4.

Again take to identical coins and put them together in the given tumbler. Shake well and throw them on the carrom board. Now note that how many times heads up (r) and (n − r ) tails up.

Observations : Part-I : Number of coins n = 1 Number of trials N = 100

29 Table 1 No. of trials

Heads up (H)

Tails up (T)

1

X

T

2

H

X

3

H

X

4

X

T

5

H

X

6

H

X

7

X

T

8

H

X

9

X

T

10

H

X

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

94

X

T

95

H

X

96

X

T

97

X

X

98

H

T

99

H

X

100

X

T

X

T

Now count the number of coins that having heads up i. e., A = …… 1 As the principle of probability of getting head up is i. e., number of times that 2 head comes (for 100 trials). 1 B = × 100 = 50 2 So, deviation in result = B − A = 50 − A Percentage of deviation =

50 − A × 100 =……% 50

30 Part-II : Now, number of coins n = 2 Number of trials N = 100 Table 2 No. of trails

Heads on both coins is up

Tails on both coins is up

Head of one is up and tail for other

1

HH

XX

XX

2

XX

XX

HT

3

XX

XX

HT

4

HH

XX

XX

5

XX

TT

XX

6

HH

XX

XX

—

—

—

—

—

—

—

—

—

—

—

—

93

XX

TT

XX

94

XX

XX

HT

95

HH

XX

XX

96

HH

XX

XX

97

XX

TT

XX

98

XX

XX

HT

99

HH

XX

XX

100

XX

XX

HT

Experimentally : Count of number of Heads-Heads up A = …… Count of number of Tails-Tails up B = …… Count of number of Head-Tail up C = …… 1 Now we know that probability of HH or HT combination is . 4 So, theoretical count of these combinations = 100 ×

1 = 25 4

31  25 − A  Now percentage deviation =   × 100 = ...... %  25  Now, theoretical probability of HT combination = Now count for 100 trails = 100 ×

1 2

1 = 50 2

So, percentage deviation of HT combination in 100 trials =

50 − C × 100 = ....% 50

Part-III : Any number of count, Let we have n = 100 number of coins Number of trials N = 100 Table 3 Trials

Head up (r)

Tails up ( h − r)

1

6

4

2

3

7

3

5

5

4

7

3

5

2

8

6

1

9

7

2

8

8

0

10

9

5

5

10

6

4

—

—

—

—

—

—

—

—

—

95

9

1

96

8

2

97

2

8

98

10

0

99

5

5

10

6

4

32 Possible Macrostates and their Deviations : Table 4 Macrostates

Frequency {y f ( r )}

Probability n! 1 ⋅ r !( n − r )! 2n

P( r ) =

Expected frequency F( r ) = P( r ) × N

Deviation = f ( r ) − f ( e)

r (Head) (h − r ) Tail 0 1 2 3 4 5 6 7 8 9 10

10 9 8 7 6 5 4 3 2 1 0

Calculations : Calculate probability P(r ) and frequency F (r ) and record in table C. Graph : Draw a curve between frequency F (r ) and r. This is shown in figure. Y

F(r)

X Fig. 12 : Graph between F (r) and r

Repeat this experiment for number of trials N = 200, 400 …… times. Now plot the curve. Now repeat whole experiment for N = 100, 200, 300, …… Conclusion : 1. For one coin we get number of times we get heads up (H ) is same as the theoretical value which is given by N × P (heads) where N is total probability and P is the probability of heads up, this is the verification of principle of priori-probability. 2. Number of times of head comes (HH ) + number of times of tails comes (TT ) + number of times of H and T both comes is always equals of total trials. 3. Percentage of deviation of head-head, tails-tails and head and tails combinations are nearly equals in both theoreticals and practical values.

33 4.

Real frequencies of observation for different combinations [r , (n − r )] this is very close to expected frequency.

Precautions : 1. Surface at which board is placed must be clean and smooth. 2. Mug/tumber should be clean and smooth. 3. Number of trials must be large.

Viva-Voce Q.1.

What do you mean by word probability ?

Ans.

This is the ratio of number of particular event to total number of event.

Q.2.

What is thermodynamical probability?

Ans.

Thermodynamical probability of a macrostate is defined as the number of microstates corresponding to that microstate.

Q.3.

What is stirling’s formula ?

Ans.

log n! = n log n − n

Q.4.

If an event completed in a times and not completed in b times then probability of event to be happen will be.  a     a + b

Ans. Q.5.

What is the total probability of an event ?

Ans.

1 (one)

Q.6.

If N similar coins are to used simultaneously a large number of times, what will be the probability of getting r heads upper most is ? N! 1 × r !( N − r)! 2N

Ans. Q.7.

What will be the most probable case in above question ?

Ans.

[50% chance] Heads up on 50% coins and tails upon sol.

Q.8.

What will be the least combination ?

Ans.

If all coins have either this or heads.

Experiment No-8 Object : To verify the cauchy’s dispersion formula. Theory : (a)

To find refractive index (µ) of a prism   A + δm   A  µ = sin   / sin     2    2  where A = angle of prism and δm is the angle of minimum deviation.

34 (b)

Cauchy’s constant If µ is refractive index of a medium corresponding to wavelength λ, according to cauchy, B …(1) µ= A+ 2 λ where A and B are cauchy’s constant. If µ 1and µ 2 are the refractive indices of a medium corresponding to wavelength λ 1 and λ 2 , B Then …(2) µ1 = A + 2 λ1 µ2 = A +

B

…(3)

λ 22

Solving equation (1) and (2), B = ( µ 1 − µ 2)λ 21λ 22/(λ 22 − λ 21) and

A = µ1 −

or

A = µ2 −

( µ 1 − µ 1)λ 21 λ 22 − λ 21 ( µ 1 − µ 2)λ 21

Procedure : (a) Setting of spectrometer 1. Direct the telescope towards some distant, a tree or a building etc. and obtain its clear and sharp image by adjusting the rack and pinion arrangement. The telescope is now set for parallel rays. Do not disturb this setting of rack and pinion arrangements through out the experiment.

λ 22 − λ 21

A

Parallel ray from collimator

To

C

B

tel e

sc op

e

2A Fig. 13

2.

Illuminate the collimator with source of light and bring telescope in line with the collimator, while 100 king through the telescope, adjust the collimator by its rack and pinion arrangement so that a sharp and well defined image of the slit is observed. Adjust the width of the collimator slit to be narrow and fine.

(b) 1. 2.

Measurement of the angle of prism Determine the least count of the spectrometer. Place the prism on the prism table such that the refractive edge A is towards the collimator and the edge A is at the centre of the prism table.

35 3.

Note down the reading (a) of the reflected light from face AB by focussing the vertical cross-wire on the reflected image of slit. Now more the telescope to other side and note down the reading (b) by focussing the vertical cross wire on the image of slit reflected from face AC. Half of the difference of two reading (a) and(b) gives the angle of prism.

4. 5. (c) 1.

sc op

e

2.

To measure angle of minimum deviation Place the prism on the table so that its centre coincides with the Collimator centre of the prism table and light B falls on one of the polished faces of the prism. In this position spectrum of the incident light will be observed from the other refracting surface. A Adjust the prism on minimum Collimator seviation position for one axis particular colour (wavelength) of the spectrum (say violet). C To procedure to find the angle of minimum seviation is as follow : Set the telescope cross wire on a Spectrum particular colour of the slit in the spectrum and go on rotating the prism table slowely keeping the Fig. 14 spectral line in view, to one side till a stage comes when the observed spectral image comes stationary and on further rotation of the table, the image moves in the backward direction. The cross wire is finally set on the spectral image when it was just stationary. Note down the reading of both the verniers. Keeping the prism table fixed, remove the prism from the prism table. Loosen the screw of telescope and bring its cross wire in line with the direct image of slit through the collimater by adjusting the tangent screw of the telescope. Take the readings of both the verniers. Repeat the experiment for prominant lines of the spectrum (say) (violet, blue, green, yellow and red). Angle of Prism : Vernier constant = ........ Te le

(i)

(ii) (iii)

3.

Vernier V1 S.No.

Telescope reading Ist face ( AB) I

1. 2. 3.

IInd face ( AC) II

Difference θ = I − II

Vernier V2 A =

θ 2

Telescope reading Ist face AB (I)

IInd face AC (II)

Difference θ = I − II

A =

θ 2

36 Mean angle of prism A = Determination of refractive index : Direct reading with vernier V1 = x 1 = …… Direct reading with vernier V2 = x 2 = ……

S. Colour λ =... No. spectral × 10−10 m line

1.

Violet

4046.8

2.

Blue

4358.3

3.

Bluesh

4916.6

4.

Green

5460.7

5.

Yellow

5769.9

6.

Orange

6152.0

Minimum deviation position

1 λ2

Angle of minimum deviation

δm2 Vernier Vernier δm1 V1 ( y1 ) V2 ( y2 ) = x1 ~y1 = x 2 − y2

µ= δm = δm1 + δm2 2

 A + δm  sin    2  A sin 2

Calculations : (Take any pair of λ 1 and λ 2 and take corresponding µ 1 and µ 2). µ 1 − (µ 1 − µ 2) λ 22

1.

A=

2.

And A = µ 2 −

λ 22 − λ 21 (µ 1 − µ 2)λ 21 λ 22 − λ 21

…

3. .....................

…(III)

4. .....................

…(IV)

Mean A = …… (µ 1 − µ 2)λ 21λ 22

(I)

B=

(II)

= ………

(III)

k = ……

(IV)

= ………

λ 22 − λ 21

…

Mean B = ......... Precautions : 1. The spectrometer should be levelled. 2. The axis of telescope and collimater should be horizontal. 3. Slit should be narrow but clear. 4. The setting of telescope for parallel ray should not be disturbed throughout the experiment.

37

Viva-voce Q.1.

Define refractive index of a medium ?

Ans.

It is the ratio of velocity in vacuum to the velocity of light in that medium.

Q.2.

What is meant by optically denser or optically rarer medium ?

Ans.

The velocity of light is more in optically rarer medium. e. g., velocity of light is more in air than that in water. So air is rarer medium than water.

Q.3.

Which colour has more velocity in vaccum ?

Ans.

Name, all the colour have the same velocity in vaccum.

Q.4. Ans.

What is Cauchy’s formula ? B µ = A+ 2 λ where A and B are constant called cauchy’s constant.

Q.5.

What is velocity of light in vaccum ?

Ans.

3 × 108 m/sec.

Q.6.

What is velocity of sound in vaccum ?

Ans.

Zero.

Q.7.

What is the formula for the resolving power of prism ? λ dµ  R. P. = l    dλ  dλ

Ans.

Where l is the length of the base of the prism. Q.8.

Why is the prism set in minimum deviation position ?

Ans.

1. In this position, the image is the brightest. 2. Magnification is unity.

Q.9.

How does the ray pass through the prism in minimum deviation position ?

Ans.

The ray passes symmetrically through the prism in this position.

Q.10.

Is sodium vapour light monochromate ?

Ans.

No, it has two wavelengths 5890 Å and 5896 Å but due to low resolving power of the prism, they appear to be merged into one.

Experiment No-9 Object : To determine the thickness of mica sheet by using Biprism. Apparatus used : An optical bench with four uprights, sodium lamp, Bi-prism, convex lens, slit and micrometer eyepiece. Formula used : The thickness of the mica sheet is given by the relation xλ t= β(µ − 1)

38 where x = displacement of the central white fringe due to the introduction of the mica sheet. λ = wavelength of light used. β = fringe width. and µ = refractive index of the material of the mica sheet for mean wavelength of white light. Method : 1. All the priliminary adjustments of the bi-prism are made as described in the previous experiment and the fringe width β for sodium light is measured. 2. The sodium lamp is then replaced by white light source, keeping all up rights fixed at their previous positions. Few coloured fringes will be observed in the field of view. 3. The vertical cross-wire is then set on the central white fringe C1 by moving the micrometer screw and the reading of the micrometer screw is noted. 4. The given mica sheet is then introduced in the path of one interfering beams. It will be observed that central white fringe of the system get shifted towards the side in which the plate had been introduced. The vertical cross wire is again set on the central white fringe C 2 and the micrometer screw reading is noted. The difference of the two readings will give the value of shift x. Mica sheet

S1x

C2

S S2x

x

C1 Plane of crosswire of the eyepiece

Fig. 15

Observations : [A] Observations for the fringe width Pitch of the micrometer screw = …… cm No of divisions on the circular head = …… ∴ Least count of the micrometer screw = ....... cm

1st position of central fringe

39 No. of fringes

Micrometer Reading (a ) cm

No. of fringes

1

21

3

23

5

25

7

27

9

29

11

31

13

33

15

35

17

37

19

39

20

41

Micro meter reading (b) cm

Width of 20 fringes cm

Mean

cm

[B] Observations for the shift x Least count of micrometer screw = …… cm Micrometer screw reading when the cross wire is set on the central wire fringe Before introducing the mica sheet (a)

After introducing the mica sheet (b)

… cm

… cm

Shift x a ~b

[C] Given data (i)

µ of mica sheet for mean white light, µ = ……

(ii)

Mean wavelength of white light λ = 6000 Å = 6 × 10−5 cm

Calculation : t=

xλ = …… cm β(µ − 1)

Result : The thickness of the given micasheet = …… cm Precautions and Sources of Error : 1. Before starting the actual measurements all the preliminary adjustments of the apparatus must be one. 2. The bench-error between the slit and the eye piece must be noted for getting the actual value of D.

40 3. 4. 5.

While finding out two conjugate positions of the lens, positions of the eye piece and bi-prism should not be changed. The slit should be narrow as possible. Imperfect removal the lateral shift of fringes.

Viva-Voce Q.1. Ans.

What do you mean by interference fringes ? They are alternate bright and dark patches of light obtained in the region of superposition of two waves trains of light.

Q.2. Ans.

What is a biprism ? A biprism is a combination of two acute angled prism placed base to base. This is made from an optically plane glass plate by proper grinding and polishing.

Q.3. Ans.

Why are refracting angles of the two prisms made so small? By doing so 2d will be small and so fringe width will be small.

Q.4. Ans.

On what factors does the fringe width depend ? The fringe width is given by λD D or β ∝ λ or β ∝ β= 2d 2d where D is the distance between two slits and eye piece and 2d is the distance between two virtual source of light.

Q.5. Ans.

What are sustained condition of interference of light ? (1) Two light source should be coherent. (2) Phase difference between two sources should be constant. (3) Size of slit should be narrow. (4) Frequency of two source should be same. (5) The source should be monochromatic.

Q.6. Ans.

Is two independent light source show interference pattern ? No.

Q.7. Ans.

How do you measure 2d ? In displacement method, 2d is given by 2d =

Q.8. Ans.

How does fringe-width depend upon the angle of biprism ? We know that 2d = 2a (µ − 1) A

d1 d2

where A is the angle of prism. λD β= 2a (µ − 1) A

i. e.,

β is inversely proportional to the angle of prism. Q.9. Ans.

What is fringe width ? Fringe width is given by β=

λD 2d

mmm