1

Chaitanya Bharathi Institute of Technology (Autonomous)

Gandipet, Hyderabad Engineering Physics notes for BE I year I Semester

(Common for all braches)

Unit – II

Interference: Introduction, Division of wavefront – Fresnel’s Biprism, Division of amplitude – Interference from thin films

(reflected light)- Newton’s rings.

Diffraction: Introduction, Distinction between Fresnel and Fraunhofer diffration, Diffraction at a single slit, Double slit,

Diffraction Grating (N Slits).

INTRODUCTION:

2

3

4

INTERFERENCE IN THIN FILMS

Also From Snell’s law

(6.17) (6.18)

5

6

7

8

DIFFRACTION

INTRODUCTION

9

10

11

12

13

14

15

16

17

18

.

19

INTERFERENCE

IMP.FORMULAE:2µtcosr = n λ: 2µtcosr = (2n+1) λ/2 : D2dark(air) = 4Rnλ : D2

dark(medium) = 𝟒𝑹𝒏𝝀

µ : 𝛌 =

𝐝𝐦𝟐 −𝐝𝐧

𝟐

𝟒𝐑(𝐦−𝐧)

1.A parallel beam of light (λ = 5890A˚) is incident on plate (µ=1.5) such that the angle of refraction into the plate is

60˚.Calculate the smallest thickness of the glass plate,which will appear dark by reflection. (Ans.3.926x10-5cm.)

2.A soap film of refractive index 1.33 is illuminated with light of different wavelengths at an angle of 45˚.There is

complete destructive interference for λ = 5890A˚.Find the thickness of the film. (Ans.3.132x10-5cm)

3.A thin film of soap solution is illuminated by white light at an angle of incidence,i =sin-1(4/5).In reflected

light,two dark consecutive overlapping fringes are observed corresponding to wavelengths 5.1x10-7m and 5x10-

7m. µ for the soap solution is 4/3. Find the thickness of the film.(Ans.1.2x10-5m)

4. .A thin film of soap solution is illuminated by white light at an angle of incidence,i =sin-1(4/5).In reflected

light,two dark consecutive overlapping fringes are observed corresponding to wavelengths 6.1x10-7m and 6.1x10-

7m. µ for the soap solution is 4/3. Find the thickness of the film. [Ans.0017cm.]

5.A thin film 4x10-5cm thick is illuminated by white light normal to its surface.Its refractive index is 1.5.What

wavelength within the visible spectrum will be intensified in the reflected beam.

6.In Newton’s rings experiment ,what will be the order of the dark ring which will have double thediameter of that

of 20 th dark ring.The wavelength of incident light is 5890 A˚ [Ans.80]

7.In Newton’s rings experiment, the diameter of the 5th and 15th rings respectively was .336 and .590cm.If the

wavelength of light is 5890 A˚. Find the radius of curvature of lens surface in contact with plane glass plate.

(Ans.99.8cm)

20

8.Newton’s ring arrangement is used with a source emitting two wavelengths λ1=6000 A˚and λ2 =4500 A˚ and it is

found that the n th dark ring due to λ1 coincides with (n+1)th dark ring for λ2 .Find the diameter of n th dark ring

of λ1 if the radius of curvature of the lens R =90cm. (OU 2002) (Ans.0.2545cm.)

9. Newton’s rings are observed in reflected light of wavelength 5900 A˚.The diameter of 10th dark ring is .50cm.

Find the radius of curvature of the lens (Ans.R=105.93cm.)

10. Newton’s rings are formed with reflected light of wavelength 5895 A˚.with a liquid between the plane and

curved surface.The diameter of the 5th dark ring is 0.3 cm and the radius of curvature of the curved surface is

100cm.Calculate the refractive index of the liquid. (Ans.1.31)

11. In Newton’s rings experiment, the diameter of the 10 th ring changes from 1.40cm to 1.20cm.when a liquid is

introduced between the lens and the plate. Calculate the refractive index of the liquid. (Ans.1.361)

12. In Newton’s rings experiment, the diameter of the 12 th ring changes from 1.50cm to 1.30cm.when a liquid is

introduced between the lens and the plate. Calculate the refractive index of the liquid. (Ans.1.331)

13. In a Newton’s rings experiment, the diameter of the 15 th ring was found to be 0.590cm.and that of the 5 th ring

was .336cm.If the radius of plano convex lens is 100cm.Calculate the wavelength of light used. (λ=5880A˚)

14. A drop of volume .02 is dropped on a surface of a tank of water of 1 sq.meter.The film spreads uniformly over

the whole surface and white light which is incident normally,is observed through spectrometer.The spectrum is

seen to contain one dark band whose centre has wavelength5500 A⁰ in air.Find the refractive index of oil.

(Ans.1.375)

15. In Newton’s rings experiment, the diameter of the4th and 12th rings respectively was .400 and .700cm. Find the

diameter of the 20 th dark ring. (Ans. .906cm.)

21

16. Newton’s rings formed by sodium light between a flat glass plate and convex lens are viewed normally.What

will be the order of the dark ring which will have double the diameter of that of 40 th dark ring.

(Ans.n=160)

17. Newton’s ring arrangement is used with a source emitting two wavelengths λ1 and λ2 and it is found that the n

th dark ring due to λ1 coincides with (n+1)th dark ring for λ2 . if the radius of curvature of the lens is R . Show

that the radius of n th dark ring of λ1 is √ λ1 λ2R/ λ1- λ2

18. Newton’s rings formed by light reflected normally from a plano convex lens and a plane glass plate with

aliquid between them.The diameter of the n th ring is 2.18mm and that of (n+10) th ring is 4.51mm.Calculate

the refractive index of the liquid,given that the radius of curvature of the lens is 90cm.and wavelength of light

used is 5893 A⁰ (Ans.1.36)

19. If the diameter of two consecutive Newton’s rings in reflected light of 5890 A⁰ are 2.0 and

2.02cm.respectively,what is the radius of curvature of the lens surface in contact with plane glass plate.

(Ans. 342.1cm.)

20.Biprism is kept 10cm away from the slit illuminated by monochromatic light of λ=5896A⁰.The width of the

fringes obtained on a screen placed at a distance of 90cmfrom the biprism is 9x10-4m.What is the distance between

two coherent sources. (Ans.6.55x10-4m)

21.In a biprism experiment,the eye piece was placed at a distance of 120cm from the source.Calculate the wavelength

of light,if the eye is required to move through a distance of 1.9cm for 20 fringes and distance between two slits is

0.06cm. (Ans. 4750 A⁰)

22.In a biprism experiment using light of wavelength 5890 A⁰,40 fringes are observed in the field of view.If this light is

replaced by light of wavelength 4358 A⁰.Calculate how many fringes are observed in the field of view. (Ans.54)

23. A biprism is placed 5cm from a slit illuminated by sodium light(λ=5890 A⁰)The width of fringes obtained on a

screen 75cm from the biprism is 9.424x10-2cm.What is the distance between two coherent sources. [Ans. 2d=0.05cm]

22

24.In a biprism experiment with a sodium light,bands of width 0.0195cm are observed at 100cm from the slit.On

introducing a convex lens 30cm away from the slit,two images of the slit are seen 0.7cm apart,at 100cm distance

from the slit.Find the wavelength of sodium light [Ans. 5850 A⁰ ]

25.Fringes are produced by a Fresnel’s biprism in the focal plane of a reading microscope which is 100cm from the

slit.A lens inserted between the biprism and microscope gives two images of the slit in two positions.In one case the

two images of the slit are 4.05mm and in the other are 2.90mm,apart.If the wavelength of sodium light is 5893 A⁰

.Find fringe width [Ans..0172cm]

26.A biprism is placed at a distance of 5cm in front of a narrow slit illuminated by a monochromatic light of

wavelength 6x10-5cm.The virtual images formed by biprism are 0.05cm apart.Find the width of the fringes formed

on a screen placed 75cm apart in front of biprism. [Ans.0.096cm ]

27.In an experiment with biprism sodium light is used and fringes 0.0196cm in width are obtained at a distance of

100cm from the slit.A convex lens is then put between the observer and the prism so as to give an image of the

source at a distance of 100cm from the slit.The distance apart of the images is found to be 0.70cm,the lens being 30

cm from the slit.Find the wavelength of Na [Ans. 5880 A⁰]

DIFFRACTION

Imp.Formulae.1.esin𝛉=nλ 2.(e+d)sin𝛉=nλ 3. (e+d)=1/N 4.nmax.=(e+d)/λ (Max.orders) 5.(e+d)/e=n/m

(absent spectra)

1.A light of wavelength 6000 A⁰is incident on a slit of variable width.Determine the width of the slit at which the

first minimum observed at 35 ⁰ (Ans. 1.06µm)

2.A slit of width 2 µm is illuminated by light of wavelength 6500 A⁰.Calculate the angle at which the first

minimum will be observed. (Ans. 18.96⁰)

23

3.The slit width in a single slit Fraunhofer diffraction is 90 µm.The screen is at a distance of 98cm.from the

slit,and the first minimum is observed at 6 µm from either side of the central maximum.Find the wavelength of

incident light. (Ans. 5510 A⁰)

4.Plane wave of wavelength 6000 A⁰ fall normally on a slit of width 0.20mm.A screen is kept at a distance 2m

from the slit.Calculate

(a)The angular position & linear width of central maxima (Ans. 6x10-3 rad & 1.2cm)

(b)The angular position of first two minima on either side of central maxima. (Ans. 6x10-3rad)

5.A diffraction grating has 6000 lines per cm.Calculate the angle between the first and second order lines for a

light of wavelength 6000A˚. (Ans.24.95˚)

6.A plane transmission grating having 6000 lines/cm is used to obtain a spectrum of light from a sodium light in

the second order.Find the angular separation between the two sodium lines whose wavelengths are 5890 A⁰ and

5896A⁰ (Ans. 0.06˚)

7.A monochromatic light of wavelength 6500 A⁰ falls normally on a grating.The first order spectrum is observed

at 15⁰ from the mean position.Calculate the grating element.Given Sin 15⁰is 0.2588 (Ans.2.512x10-6m)

8.In an experiment with grating,3 rd order spectral line of wavelength λ coincides with the 4 th order spectral

line of wavelength 4992A⁰.Calculate the value of λ. (Ans.6656 A⁰)

9.In the spectrum of diffraction grating used for normal incidence,green line(λ=5400 A⁰)in some order coincides

with the next higher order of violet (λ=4050 A⁰).If the angle of diffraction is 30⁰.Find the grating element and

no.of lines in 1cm.length of grating. (Ans. e+d=3.24x10-4cm&N=3086)

24

10.How many orders will be visible if the wavelength of the incident radiation is 5000A˚and number of lines on

the grating is 2620 in one inch. (Ans. n≥19 )

11.A grating has 6000 lines/cm.Calculate the angular separation of the two mercury lines of wavelengths

5770A°and 5461A° in the first order spectrum.

12.In relation to a plane transmission grating 5000 lines/cm.Answer the following

(a)For wavelength 6000A˚what is the highest order of spectrum which may be observed.

(b)If opaque spaces are exactly 2 times the transparent spaces,which order of specta

Will be absent. (Ans. a.n=3.33 & b.3,6,9----)

13. Light of wavelength 6000A˚ falls on a screen at a distance of 100cm.from a narrow slit.Find the width of the

slit if the first minima lie 1mm on either side of the central maximum. (Ans. 0.06cm.)

14.In a plane transmission grating the angle of diffraction for the second order principle maximum for the

wavelength 5000A˚ is 30˚.Calculate the number of lines in 1cm of the grating surface. (Ans.1000)

15.What is the highest order spectrum,which may be seen with monochromatic light of wavelength 6000A˚ by

means of diffraction grating with 5000lines/cm. (Ans.3)

16.A plane diffraction grating has the value of grating constant equal to 15x10-4cm.Calculate the position of third

order maximum for λ=2.4x10-4cm. (Ans. 28.7˚)

25

17.The third order diffracted image,corresponding to a wavelength of 4400A˚,coincides with the second order

image corresponding to an unknown wavelength in the spectrum produced by grating.Find the unknown

wavelength. (Ans.6600A˚)

18.A grating has 6000lines/cm.Find the angular separation of two yellow lines of mercury of wavelengths 5770A˚

and 5791A˚ in the second order. (Ans.11’)

19.Show that the grating with 5000 lines/cm cannot give a spectrum in the fourth higher orders for light of

wavelength 5890A˚

20.A diffraction grating used at normal incidence gives a line λ=6250A˚in a certain order superimposed on

another line λ=5000A˚ of the next higher order.If the angle of diffraction is 30˚,how many lines are there to one

cm in the grating. (Ans.2000)

21. A monochromatic light of wavelength 6560 A⁰ falls normally on a grating 2cm wide.The first order spectrum

is produced at an angle 18˚14’ from the normal.What is the total number of lines on the grating. Given Sin 18˚14’

=0.3129. (Ans.9541)

22.Calculate the missing orders in a double slit Fraunhofer diffraction,if the widths of slits are 0.08x10-3m and

they are 0.4x08x10-3m apart. (Ans.n=6m 6,12,18……etc. m=1,2,3…….)

23.What is the highest order spectrum which may be seen with monochromatic light of wavelength 5000 A˚by

means of diffraction grating with 5000lines/cm. (Ans.4)

26