Vardaan Institute - Physics Worksheet (Level 1)

Topic 1: Huygens Principle & Wavefronts

Define a wavefront. Use Huygens' geometrical construction to show the propagation of a plane wavefront in a medium.

Differentiate between spherical and plane wavefronts on the basis of source distance and variation of amplitude with distance.

Draw the shape of the wavefront when a plane wavefront is incident on (i) a thin convex lens and (ii) a concave mirror.

AI Prompt: Create a mathematically correct physics ray diagram showing a plane wavefront (vertical parallel lines) incident on a thin biconvex lens, emerging as a converging spherical wavefront. Below it, show a plane wavefront incident on a concave mirror, reflecting as a converging spherical wavefront. Background fully white. Landscape mode. High quality lines.

File Name: Level1_Q3_WavefrontLensMirror.png

Using Huygens' principle, derive Snell’s law of refraction for a plane wave incident on a plane surface separating two media.

A plane wave of wavelength $600 \text{ nm}$ is incident on a glass slab ($n=1.5$). Calculate the wavelength and speed of light inside the glass.

Verify the laws of reflection using Huygens' principle. Draw a neat labelled diagram for the same.

Why does light travel slower in a denser medium? Explain based on the wave theory of light.

Show that during refraction, the frequency of light remains unchanged while the wavelength changes.

Light of wavelength $5000 \text{ \AA}$ travels from vacuum into a medium of refractive index $1.33$. Find the phase difference between two points on a ray separated by $2 \text{ cm}$ in the medium.

10.

State the conditions under which a spherical wavefront can be approximated as a plane wavefront.

Topic 2: Interference of Light & YDSE

11.

What are coherent sources? Why are they necessary for observing a stable interference pattern?

12.

In Young's Double Slit Experiment, derive an expression for the fringe width ($\beta$).

13.

Two coherent sources have intensities $I$ and $4I$. Find the maximum and minimum resultant intensities in the interference pattern.

14.

In a YDSE, the distance between the slits is $0.2 \text{ mm}$ and the screen is at $1.5 \text{ m}$. If the 4th bright fringe is at $1.2 \text{ cm}$ from the central maximum, find the wavelength of light used.

15.

What happens to the fringe width if (i) the screen is moved further away, (ii) monochromatic light is replaced by white light, and (iii) the whole apparatus is immersed in water ($n=4/3$)?

16.

A beam of light consisting of two wavelengths $650 \text{ nm}$ and $520 \text{ nm}$ is used to obtain interference fringes in YDSE. Find the least distance from the central maximum where the bright fringes of both wavelengths coincide. (Given $D=1.2 \text{ m}$ and $d=2 \text{ mm}$).

17.

Explain why the intensity of the central fringe in YDSE is four times the intensity of a single slit.

18.

Find the ratio of intensities at two points on a screen in YDSE where the path difference is $\lambda/6$ and $\lambda/3$.

19.

The ratio of widths of two slits in YDSE is $4:1$. Find the ratio of $I_{max}$ to $I_{min}$ in the interference pattern.

20.

Show that the average intensity in the interference pattern is equal to the sum of intensities of the two individual waves.

Topic 3: Diffraction of Light

21.

What is diffraction of light? Under what condition is it clearly observable?

22.

Describe the diffraction pattern obtained with a single slit. Derive the condition for the first minimum and first secondary maximum.

23.

A single slit of width $0.1 \text{ mm}$ is illuminated by monochromatic light of wavelength $600 \text{ nm}$. Find the angular width of the central maximum.

24.

How does the width of the central maximum in single slit diffraction change when (i) slit width is halved, and (ii) distance to the screen is doubled?

25.

Compare interference and diffraction patterns to bring out any three differences between them.

26.

Light of wavelength $500 \text{ nm}$ is incident on a slit of width $0.2 \text{ mm}$. Find the linear width of the central maximum on a screen kept $2 \text{ m}$ away.

27.

Sketch a graph showing the intensity distribution in single slit diffraction as a function of the path difference ($a \sin \theta$).

AI Prompt: Create a mathematically accurate physics graph showing the intensity distribution for single-slit diffraction. The x-axis should be 'path difference' (a sin theta) or 'angle'. The central maximum should be very wide and intense. Secondary maxima should be significantly smaller and narrower. Label axes clearly. White background. Landscape mode.

File Name: Level1_Q27_DiffractionIntensityGraph.png

28.

Estimate the distance for which ray optics is a good approximation for an aperture of $4 \text{ mm}$ and wavelength $400 \text{ nm}$. (Fresnel Distance).

29.

Explain why a person sitting behind a pillar can hear a conversation on the other side, but cannot see the speakers.

30.

What is the condition for a $n^{th}$ order minimum in single slit diffraction? How many minima are possible for a slit of width $a = 3.5\lambda$?

Topic 4: Polarization

31.

Explain the phenomenon of polarization of light. Which type of waves (transverse or longitudinal) can be polarized?

32.

State Malus's Law. A polarizer and analyzer are oriented at $45^\circ$ to each other. Calculate the ratio of the intensity of transmitted light to the incident polarized light.

33.

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

34.

A ray of light is incident on a glass plate at the polarizing angle. If the refractive index of glass is $1.732$, calculate the angle of refraction.

35.

Define Plane of Vibration and Plane of Polarization. How are they related?

36.

Unpolarized light of intensity $I_0$ is incident on a Polaroid. What is the intensity of light transmitted through it? If this transmitted light passes through another Polaroid whose axis is at $30^\circ$ to the first, what is the final intensity?

37.

Describe how polarization by scattering occurs in the atmosphere. Why is the sky blue and the light from the sky partially polarized?

AI Prompt: Create a mathematically accurate physics diagram showing polarization by scattering. Incident unpolarized light hits a gas molecule, and scattered light in the perpendicular direction is shown as plane polarized. Use standard arrow and dot notation for E-field vectors. Background white. Landscape mode.

File Name: Level1_Q37_ScatteringPolarization.png

38.

Calculate the angle of incidence for which the light reflected from water ($n=1.33$) will be completely polarized.

39.

Explain two practical applications of Polaroids in everyday life.

40.

At what angle should two Polaroids be placed so that the intensity of transmitted light is $1/8^{th}$ of the intensity of the incident unpolarized light?

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