Vardaan Institute - Wave Optics Worksheet (Level 2)

Topic 1: Huygens Principle & Wave Theory

State Huygens’ Principle of wave propagation. Explain how a new wavefront is constructed at a later time $t$ from a given primary wavefront.

Using Huygens' wave theory, prove the laws of reflection of light at a plane surface. Draw a neat labelled diagram.

Derive Snell’s law of refraction using the wave theory of light. Explain why wavelength decreases when light enters an optically denser medium.

Show the refraction of a plane wavefront through a prism and a thin convex lens using Huygens' construction.

AI Prompt: Create a mathematically accurate physics ray diagram showing a plane wavefront incident on a glass prism and a biconvex lens. Show the delayed propagation through the thicker parts of the glass, resulting in the tilting of the wavefront for the prism and the curving of the wavefront for the lens. Background must be fully white. Landscape mode. High quality resolution.

File Name: Level2_Q4_HuygensRefraction.png

Light of wavelength $589 \text{ nm}$ is incident from air on a water surface. What are the wavelength, frequency, and speed of (a) reflected and (b) refracted light? (Refractive index of water $= 1.33$).

What is the shape of the wavefront in the following cases: (a) Light diverging from a point source, (b) Light emerging out of a convex lens when a point source is placed at its focus, (c) A small portion of the wavefront of light from a distant star intercepted by the Earth.

The speed of light in a medium is $2 \times 10^8 \text{ m/s}$. If the wavelength of light in vacuum is $6000 \text{ \AA}$, find its wavelength in the medium.

Explain why the backwave is not observed in Huygens' construction based on the obliquity factor.

A plane wavefront is incident at an angle of $30^\circ$ on a glass slab. Find the angle made by the refracted wavefront with the interface if the refractive index of glass is $1.5$.

10.

Does the verification of laws of reflection/refraction by wave theory depend on the intensity of light? Justify.

Topic 2: Interference of Light & YDSE

11.

Derive the expression for the intensity at a point in the interference pattern of two waves having amplitudes $a_1$ and $a_2$ and phase difference $\phi$.

12.

Define Fringe Width. Derive the expression $\beta = \frac{\lambda D}{d}$ for the fringe width in Young's Double Slit Experiment.

13.

Two sources of intensity $I$ and $9I$ interfere at a point. Calculate the resultant intensity when the phase difference is (a) $0$, (b) $\pi$, and (c) $\pi/2$.

14.

In a YDSE, the slits are separated by $0.28 \text{ mm}$ and the screen is placed $1.4 \text{ m}$ away. The distance between the central bright fringe and the fourth bright fringe is measured to be $1.2 \text{ cm}$. Determine the wavelength of light used.

15.

Describe the interference pattern obtained with white light in YDSE. What is the color of the central fringe?

16.

Two coherent light beams of intensity $I$ and $4I$ are superposed. What are the maximum and minimum possible intensities in the resulting pattern? Also, find the visibility of the fringes.

17.

In YDSE, if one slit is covered with a thin transparent sheet of thickness $t$ and refractive index $\mu$, find the expression for the shift of the central fringe.

18.

Draw a graph showing the variation of intensity with the path difference in YDSE. Compare it with the intensity distribution in single slit diffraction.

AI Prompt: Create a mathematically accurate physics graph showing the intensity distribution of YDSE (equally spaced peaks of same height) vs. Single Slit Diffraction (wide central peak with rapidly decaying side peaks). Overlay them or place side by side for comparison. Background white. Landscape mode.

File Name: Level2_Q18_InterferenceVsDiffractionGraph.png

19.

Calculate the ratio of intensities at points $P$ and $Q$ on a screen in YDSE, where waves from two slits have a path difference of (a) $0$ and (b) $\lambda/4$.

20.

Why is the interference pattern not observed when two independent monochromatic sources are used?

21.

A beam of light consisting of two wavelengths $650 \text{ nm}$ and $520 \text{ nm}$ is used to obtain fringes in YDSE. What is the least distance from the central maximum where the bright fringes of both wavelengths coincide? (Take $D = 120 \text{ cm}, d = 2 \text{ mm}$).

22.

How is the fringe width affected if the distance between the slits is reduced to one-third?

23.

In YDSE, the distance between the first and tenth bright fringe is $18 \text{ mm}$. When the whole apparatus is immersed in a liquid, the distance becomes $12.6 \text{ mm}$. Find the refractive index of the liquid.

Topic 3: Diffraction of Light

24.

What is the main difference between Fresnel and Fraunhofer diffraction? Derive the condition for the minima in Fraunhofer diffraction at a single slit.

25.

A slit of width 'a' is illuminated by light of wavelength $700 \text{ nm}$. For what value of 'a' will the first minimum fall at an angle of $30^\circ$?

26.

Find the angular width of the central maximum in single slit diffraction if the slit width is $0.2 \text{ mm}$ and wavelength is $500 \text{ nm}$.

27.

A screen is placed $2 \text{ m}$ away from a single slit of width $0.1 \text{ mm}$. If the first minimum is at a distance of $5 \text{ mm}$ from the central maximum, calculate the wavelength of light.

28.

Distinguish between the interference pattern in YDSE and the diffraction pattern in a single slit. Mention at least three points.

29.

Why is the central maximum in diffraction wider than the secondary maxima? Show this using a diagram of the pattern.

30.

For what distance is ray optics a good approximation when the aperture is $3 \text{ mm}$ wide and the wavelength is $500 \text{ nm}$?

31.

Determine the resolving power of a telescope whose objective has a diameter of $5 \text{ m}$ for light of wavelength $550 \text{ nm}$.

32.

Two point sources are $10 \text{ mm}$ apart and are at a distance of $100 \text{ m}$ from a telescope. What should be the minimum diameter of the objective to resolve them? ($\lambda = 500 \text{ nm}$).

33.

State Rayleigh’s criterion for resolution. How does the resolving power of a microscope change if the medium between the object and objective is changed from air to oil?

Topic 4: Polarization

34.

What is meant by the polarization of light? Explain with a diagram how a Polaroid acts as a filter.

35.

State Malus’s Law. Two Polaroids are oriented such that the intensity of light transmitted by them is maximum. Through what angle should one of them be rotated so that the intensity becomes half of the maximum?

36.

A ray of light is incident on the surface of a glass plate of refractive index $1.55$ at the polarizing angle. Calculate the angle of refraction.

37.

State Brewster's Law. Prove that when light is incident at the polarizing angle, the reflected and refracted rays are perpendicular to each other.

AI Prompt: Create a mathematically accurate physics diagram for Brewster's Law. Incident unpolarized light strikes a glass surface at Brewster's angle. Show the reflected ray as fully plane polarized and the refracted ray as partially polarized. Label the angle between reflected and refracted ray as 90 degrees. Background white. Landscape mode.

File Name: Level2_Q37_BrewstersLawPerp.png

38.

Unpolarized light of intensity $I_0$ passes through three Polaroids such that the transmission axis of the last Polaroid is perpendicular to the first. If the middle Polaroid is at $45^\circ$ to the first, find the final transmitted intensity.

39.

How can you distinguish between unpolarized and plane polarized light using a Polaroid?

40.

The critical angle for a certain medium is $45^\circ$. What is the polarizing angle for this medium?

41.

Explain the use of Polaroids in (a) Sunglasses and (b) 3D movie spectacles.

42.

Show that if unpolarized light is incident on a Polaroid, the transmitted intensity is exactly half of the incident intensity.

43.

Calculate the angle between two Polaroids if the intensity of light coming out of the second is $1/8$ of the intensity of unpolarized light incident on the first.

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