# Assignments Class 12 Physics Wave Optics

Please refer to Assignments Class 12 Physics Wave Optics Chapter 10 with solved questions and answers. We have provided Class 12 Physics Assignments for all chapters on our website. These problems and solutions for Chapter 10 Wave Optics Class 12 Physics have been prepared as per the latest syllabus and books issued for the current academic year. Learn these solved important questions to get more marks in your class tests and examinations.

## Wave Optics Assignments Class 12 Physics

Question: A diffraction pattern is obtained by using beam of red light what will happen, if red light is replaced by the blue light?
(a) Bands disappear.
(b) Bands become broader and farther apart.
(c) No change will take place.
(d) Diffraction bands become narrow and crowded together.

D

Question:  A screen is placed 50 cm from a single slit which is illuminated with light of avelength 6000 Å. If the distance between the first and third minima in the diffraction pattern is 3.0 mm. The width of the slit is
(a) 1 × 10–4 m
(b) 2 × 10–4 m
(c) 0.5 × 10–4 m
(d) 4 × 10–4 m

B

Question:  In a double slit experiment using light of wavelength 600 nm, the angular width of a fringe on a distant screen is 0.1°. The spacing
between the two slits is
(a) 3.44 × 10–4 m
(b) 1.54 ×  10–4  m
(c) 1.54 × 10–3 m
(d) 1.44 × 10–3 m

A

Question:  A Young’s double slit experiment uses a monochromatic source of light. The shape of interference fringes formed on the screen is
(a) parabola
(b) straight line
(c) circle
(d) hyperbola

D

Question:  A parallel beam of sodium light of wavelength 5890 Å is incident on a thin glass plate of refractive index 1.5 such that the angle of refraction in the plate is 60°. The smallest thickness of the plate which will make it dark
by reflection
(a) 3926 Å
(b) 4353 Å
(c) 1396 Å
(d) 1921 Å

A

Question:  Which of the following is correct for light diverging from a point source?
(a) The intensity decreases in proportion for the distance squared.
(b) The wavefront is parabolic.
(c) The intensity at the wavelength does not depend on the distance.
(d) None of these.

A

Question:  Consider the following statements in case of Young’s double slit experiment.
(1) A slit S is necessary if we use an ordinary extended source of light.
(2) A slit S is not needed if we use an ordinary but well collimated beam of light.
(3) A slit S is not needed if we use a spatially coherent source of light.
Which of the above statements are correct?
(a) (1), (2) and (3)
(b) (1) and (2) only
(c) (2) and (3) only
(d) (1) and (3) only

A

Question:  The colours seen in the reflected white light from a thin oil film are due to
(a) Diffraction
(b) Interference
(c) Polarisation
(d) Dispersion

B

Question: In a Young’s double slit experiment an electron beam is used to obtain interference pattern. If the spread of electron is decreases then
(a) distance between two consecutive fringes remains the same
(b) distance between two consecutive fringes decreases
(c) distance between two consecutive fringes increases
(d) none of these

C

Question: In young’s double slit experiment using monochromatic light of wavelengths l, the intensity of light at a point on the screen with path difference is λ is M unit. The intensity of light at a point where path difference is λ/3 is
(a) M/2
(b)M/4
(c)M/8
(d)M/16

B

Question: In a double slit experiment the distance between slits is increased ten times whereas their distance from screen is halved then the fringe width is
(a) becomes 1/20
(b) becomes1/90
(c) it remains same
(d) becomes1/10

A

Question: In a two slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by 5 × 10–2 m towards the slits, the change in fringe width is 3 × 10–5 m. If the distance between slits is 10–3 m, the wavelength
of light will be
(a) 3000 Å
(b) 4000 Å
(c) 6000 Å
(d) 7000 Å

C

Question: Two slits in young’s double slit experiment have widths in the ratio 81 : 1. The ratio of the amplitudes of light waves is
(a) 3 : 1
(b) 3 : 2
(c) 9 : 1
(d) 6 : 1

C

Question: The fringe width in a young’s double slit interference pattern is 2.4 × 10–4 m, when red light of wavelength 6400 Å is used. How much will it change, if blue light of wavelength 4000 Å is used ?
(a) 0.9 × 10–4 m
(b) 1.5 × 10–4 m
(c) 4.5 × 10–4 m
(d) 0.45 × 10–4 m

A

Question:Interference fringes were produced in Young’s double slit experiment using light of wavelength 5000 Å. When a film of material 2.5 × 10–3 cm thick was placed over one of the slits, the fringe pattern shifted by a distance equal to 20 fringe widths. The refractive index of the material of the film is
(a) 1.25
(b) 1.33
(c) 1.4
(d) 1.5

C

Question: In Young’s double slit experiment two disturbances arriving at a point P have phase difference of Π/3 . The intensity of this point expressed as a fraction of maximum intensity I0 is
(a) 3/2 I0
(b)1 /2 I0
(c) 4/3 I0
(d)3/4 I

D

Question: In the case of light waves from two coherent sources S1 and S2, there will be constructive interference at an arbitrary point P, the path difference S1P – S2P is

B

Question: A plane wave passes through a convex lens.
The geometrical shape of the wavefront that emerges is
(a) plane
(b) diversing spherical
(c) converging spherical
(d) none of these

C

Question: Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is π/2 at point A and p at point B. Then the difference between the resultant intensities at A and B is
(a) 2I
(b) 4I
(c) 5I
(d) 7I

B

Question: In a double slit experiment, the distance between the slits is d. The screen is at a distance D from the slits. If a bright fringe is formed opposite to one of the sl its, its order is

D

Question: Consider sunlight incident on a slit of width 104 Å. The image seen through the slit shall
(a) be a fine sharp slit white in colour at the centre
(b) a bright slit white at the centre diffusing to zero intensities at the edges
(c) a bright slit white at the centre diffusing to regions of different colours
(d) only be a diffused slit white in colour

A

Assertion & Reasoning Based MCQs
two statements are given-one labelled Assertion (A) and the other labelled Reason (R).
Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

Question: Assertion (A) : Diffraction is common in sound but not common in light waves.
Reason (R): Wavelength of light is more than the wavelength of sound.

C

Question: Assertion (A) : In Young’s double slit experiment, the fringes become indistinct if one of the slits is covered with cellophane paper.
Reason (R) : The cellophane paper decrease the wavelength of light.

C

Question: Assertion (A) : The film which appears bright in reflected system will appear dark in the transmitted light and vice-versa.
Reason (R) : The conditions for film to appear bright or dark in reflected light are just reverse to those in the transmitted light.

A

Question: Assertion (A) : When tiny circular obstacle is placed in the path of light from some distance, a bright spot is seen at the centre of the shadow
of the obstacle.
Reason (R) : Destructive interference occurs at the centre of the shadow.

C

Question:State Huygens principle of diffraction of light.
Answer : According to Huygens’ principle, each point on a wavefront is a source of secondary waves, which add up to give a wavefront at any later time.

Question: Define the term ‘coherent sources’ which are required to produce interference pattern in Young’s double slit experiment.
Answer : Two sources are said to be coherent, if they emit light waves of same frequency or wavelength and of a constant phase difference.

Question: In a Young’s double slit experiment, the fringe width is found to be 0.12 mm. If the whole apparatus is immersed in water of refractive index (4/3), without disturbing the geometrical arrangement, what is the new fringe width?

Question: Is Huygens principle valid for longitudinal sound waves?
Answer : Yes, Huygen’s principle is valid for longitudinal as well as transverse waves and for all wave phenomena.

Question: How does the angular separation between fringes in single-slit diffraction experiment change when the distance of separation between the slit and screen is doubled.
Answer : In a single slit diffraction separation between fringes θ∝nλ/a So, there is no effects on angular separation 2θ by changing of the distance of separation ‘D’ between slit and the screen.

Question: In a two-slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by 5×10–2 m towards the slits, the change in fringe width is 3 ×10–5. If the distance between the slits is 10–3 m, calculate the wavelength of the light used.

Question: Light of wavelength 6 × 10–5 cm falls on a screen at a distance of 100 cm from a narrow slit.
Find the width of the slit if the first minima lies 1 mm on either side of the central maximum.

Question: The intensity of the light coming from one of the slits in a YDSE is double the intensity from the other slit. Find the ratio of maximum intensit y to minimum intensity in the interference fringe pattern observed.

Question: A soap film of thickness 0.3 mm appears dark when seen by the reflected light of wavelength 580 nm. What is the index of refraction of the soap solution,if it is known to be between 1.3 and 1.5?

Question: A slit of width a is illuminated by light of wavelength 6000 Å. For what value of a will the (i) First maximum fall at an angle of diffraction of 30°
(ii) First minimum fall at an angle of diffraction 30°?

Question: Two wavelengths of sodium light 590 nm and 596 nm are used, in turn to study the diffraction taking place at a single slit of aperture 2 ×10–4 m.
The distance between the slit and the screen is 1.5 m. Calculate the separation between the positions of the first maxima of the diffraction pattern obtained in the two cases.

Question: In a single slit diffraction experiment first minimum for λ1 = 660 nm coincides with first maxima for wavelength λ2. Calculate λ2.

Question: Laser light of wavelength 640 nm incident on a pair of slits produces an interference pattern in which the bright fringes are separated by 7.2 mm. Calculate the wavelength of another source of light which produces interference fringes separated by 8.1 mm using same arrangement.
Also find the minimum value of the order (n) of bright fringe of shorter wavelength which coincides with that of the longer wavelength.

Question: In a YDSE, the slits are 2 mm apart and are illuminated with a mixture of two wavelengths λ = 750 nm and λ′ = 900 nm. At what distance from the common central bright fringe on a screen 2 m from the slits will a bright fringe from one interference pattern coincide with a bright fringe from the other?

Question: Explain the following, giving reasons: (i) When light travels from a rarer to a denser medium, the speed decreases. Does this decrease in speed imply a reduction in the energy carried by the wave ?
(ii) In the wave picture of light, intensity of light is determined by the square of the amplitude of the wave. What determines the intensity in the photon picture of light?

Question: (a) In a single slit diffraction pattern, how does the angular width of the central maximum vary, when
(i) aperture of slit is increased?
(ii) distance between the slit and the screen is decreased?
(b) How is the diffraction pattern different from the interference pattern obtained in Young’s double slit experiment?

(ii) Effect of distance between slit and screen (D) : From the equation (i), it follows that 2θ0 is independent of D. So the angular width will emain same whatever the value of D.
(b) Difference between interference and diffraction experiment to observe diffraction pattern

Question: Yellow light (l = 6000 Å) illuminates a single slit of width 1 ×10–4 m. Calculate the distance between two dark lines on either side of the central maximum, when the diffraction pattern is viewed on a screen kept 1.5 m away from the slit.

Question: (a) What is the effect on the interference fringes in a Young’s double slit experiment when (i) the separation between the two slits is decreased?
(ii) the width of the source slit is increased?
(b) The intensity at the central maxima in Young’s double slit experimental set-up is I0.
Show that the intensity at a point where the path difference is l/3 is I0/4.

Question: (a) Use Huygen’s geometrical construction to show how a plane wave-front at t = 0 propagates and produces a wave-front at a later time.
(b) Verify, using Huygen’s principle, Snell’s law of refraction of a plane wave propagating from a denser to a rarer medium.
(c) When monochromatic light is incident on a surface separating two media, the reflected and refracted light both have the same frequency.
Explain why.
Answer:(a) Consider a spherical or plane wavefront moving towards right. Let AB be its position at any instant of time.
The region on its left has received the wave while region on the right is undisturbed.

Huygens geometrical construction for the propagation of (a) spherical, (b) plane wavefront.
According to Huygens principle, each point on AB becomes a source of secondary disturbance, which takes with the same speed c. To find the new wavefront after time t, we draw spheres of radii ct, from each point on AB.
The forward envelope or the tangential surface CD of the secondary wavelets gives the new wavefront after time t.
The lines aa′, bb′, cc′, etc., are perpendicular to both AB and CD. Along these lines, the energy flows from AB to CD.
So these lines represent the rays. Rays are always normal to wavefronts.
(b) A source of light sends the disturbance in all the directions and continuous locus of all the particles vibrating in same phase at any instant is called as wavefront.
Given figure shows the refraction of a plane wavefront at a rarer medium i.e., v2 > v1

The incident and refracted wavefronts are shown in figure.
Let the angles of incidence and refraction be i and r respectively.
From right DABC, we have,

(a constant)
This verifies Snell’s law of refraction. The constant 1µ2 is called the refractive index of the second medium with respect to first medium.
(c) Reflection and refraction arise through interaction of incident light with atomic constituents of matter which vibrate with the same frequency as that of the incident light.
Hence frequency remains unchanged.

Question: (a) Using Huygens ’ construcion of secondary wavelets explain how a diffraction pattern is obtained on a screen due to a narrow slit on which a monochromatic beam of light is incident normally.
(b) Show that the angular width of the first diffraction fringe is half that of the central fringe.
(c) Explain why the maxima at Φ =[ n+1/2]λ/a become weaker and weaker with increasing n.
Answer: (a) Waves diffract when they encounter obstacles. A wavefront impinging on a barrier with a slit in it, only the points on the wavefront that move into the slit can continue emitting forward moving waves but because a lot of the wavefront has been blocked by the barrier, the points on the edges of the hole emit waves that bend round the edges.

Before the wavefront strikes the barrier the wavefront generates another forward moving wavefront. Once the barrier blocks most of the wavefront the forward moving wavefront bends around the slit because the secondary waves they would need to interfere with to create a straight wavefront have been blocked by the barrier.
According to Huygen’s principle, each point on the wavefront moving through the slit acts like a point source. We can think about some of the effect of this if we analyse what happens when two point sources are close together and emit wavefronts with the same wavelength and frequency. These two point sources represent the point sources on the two edges of the slit and we can call the source A and source B
as shown in the figure.
Each point source emits wavefronts from the edge of the slit. In the diagram we show a series of wavefronts emitted from each point source. The continuous lines show peaks in the waves emitted by the point sources and the dotted lines represent troughs. We label the places where constructive interference (peak meets a peak or trough meets a trough) takes place with a solid diamond and places where destructive interference (trough meets a peak) takes place with a hollow diamond. When the wavefronts hit a barrier there will be places on the barrier where constructive interference takes place and places where destructive interference happens.

The measurable effect of the constructive or destructive interference at a barrier depends on what type of waves we are dealing with.
(b) Condition for nth secondary dark fringe :

Light rays which on passing through the slit of width ‘a’ get diffracted by an angle q1, such that the path difference between extreme rays on emerging from slit is a sin θ1 = λ Then the waves from first half and second half of slit have a path difference of l/2, so they interfere destructively at point P on screen, forming first secondary dark fringe.
Thus condition for first secondary dark fringe or first secondary minimum is
sin θ1 = λ/a

Case Based MCQs

Hnygen Principle
Huygen principle is the basis of wave theory of light. Each point on a wavefront  acts as a fresh source of new disturbance, called secondary waves or wavelets. The secondary wavelets spread out in all directions with the speed light in the given medium.
An initially parallel cylindrical beam travels in a medium of refractive index μ(I) = μ0 + μ2I, where μ0 and μ2 are positive constants and I is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius

Question: According to Huygens Principle, the surface of constant phase is
(a) called an optical ray
(b) called a wave
(c) called a wavefront
(d) always linear in shape

C

Question: The initial shape of the wavefront of the beam is
(a) planar
(b) convex
(c) concave
(d) convex near the axis and concave near the periphery

A

Question: As the beam enters the medium, it will
(a) travel as a cylindrical beam
(b) diverge
(c) converge
(d) diverge near the axis and converge near the periphery.