Vardaan Institute - Physics Worksheet (Level 1)

Topic 1: Reflection & Spherical Mirrors

Define the principal focus and focal length of a concave mirror. Use a ray diagram to support your answer.

AI Prompt: Create a mathematically correct physics ray diagram showing the principal focus of a concave mirror. Show multiple parallel rays incident on the concave mirror and reflecting to converge exactly at the Focus (F). Label Pole (P), Focus (F), Center of Curvature (C), and focal length (f). The background of the whole image should be fully white. It should be in landscape mode. High quality, clean lines.

File Name: Level1_Q1_ConcaveFocusDiagram.png

Derive the mirror formula $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ for a concave mirror producing a real, inverted image.

An object is placed at a distance of $15\text{ cm}$ from a concave mirror of radius of curvature $20\text{ cm}$. Find the position, nature, and magnification of the image.

Give two reasons why a convex mirror is used as a rear-view mirror in vehicles.

A convex mirror used for rear-view on an automobile has a radius of curvature of $3.00\text{ m}$. If a bus is located at $5.00\text{ m}$ from this mirror, find the position, nature, and size of the image.

Draw a neat ray diagram to show the formation of a virtual, erect, and magnified image by a concave mirror. Write the position of the object for this case.

AI Prompt: Create a mathematically correct physics ray diagram showing a concave mirror forming a virtual, erect, and magnified image. Object between P and F. Show extending reflected rays behind mirror. Fully white background, landscape mode, high quality.

File Name: Level1_Q6_ConcaveMirrorVirtual.png

An object of size $7.0\text{ cm}$ is placed at $27\text{ cm}$ in front of a concave mirror of focal length $18\text{ cm}$. At what distance from the mirror should a screen be placed so that a sharp focused image can be obtained?

Find the focal length of a convex mirror whose radius of curvature is $32\text{ cm}$. Also find its magnification when an object is placed $16\text{ cm}$ from it.

A concave mirror produces three times magnified (enlarged) real image of an object placed at $10\text{ cm}$ in front of it. Where is the image located?

10.

A concave mirror produces a virtual image three times the size of the object. If the focal length is $15\text{ cm}$, find the object distance.

Topic 2: Refraction & Total Internal Reflection

11.

State the laws of refraction of light (Snell's Law).

12.

Light travels from air into glass of refractive index $1.5$. If the angle of incidence is $45^\circ$, calculate the angle of refraction. ($\sin 45^\circ = 0.707$)

13.

Define critical angle. Derive the relation between the critical angle and the refractive index of a medium.

14.

Explain with a ray diagram what is meant by 'lateral shift' when light passes through a rectangular glass slab.

AI Prompt: Create a mathematically correct physics ray diagram showing refraction of light through a rectangular glass slab. Show incident, refracted, and emergent rays. Clearly label the lateral displacement (shift) between the extended incident ray and emergent ray. Fully white background, landscape mode.

File Name: Level1_Q14_GlassSlabLateralShift.png

15.

A tank is filled with water to a height of $12.5\text{ cm}$. The apparent depth of a needle lying at the bottom is measured to be $9.4\text{ cm}$. What is the refractive index of water?

16.

The refractive index of glass is $1.5$ and that of water is $1.33$. What is the critical angle for a ray of light traveling from glass to water?

17.

The speed of light in a transparent medium is $2 \times 10^8\text{ m/s}$. Find the critical angle for this medium-vacuum interface.

18.

A mark at the bottom of a liquid filled beaker appears to rise by $0.1\text{ m}$. If the depth of the liquid is $1\text{ m}$, find the refractive index of the liquid.

19.

Explain the working principle of optical fibers. Why is the refractive index of the core kept higher than that of the cladding?

20.

Draw a neat labelled diagram showing Total Internal Reflection in an optical fiber.

AI Prompt: Create a mathematically correct physics ray diagram showing Total Internal Reflection inside an optical fiber core. Show core, cladding, a light ray entering, and bouncing off walls (TIR). Fully white background, landscape mode.

File Name: Level1_Q20_OpticalFiberTIR.png

21.

Briefly explain the formation of a mirage in a desert on a hot summer day using the concept of TIR.

Topic 3: Lenses & Lens Maker's Formula

22.

Write the Lens Maker's formula. Explain the sign convention used for the radii of curvature ($R_1$ and $R_2$) for a biconvex lens.

23.

A biconvex lens is made of glass of refractive index $1.5$. The radii of curvature of its two surfaces are $20\text{ cm}$ and $30\text{ cm}$ respectively. Calculate its focal length.

24.

A double concave lens has a focal length of $-15\text{ cm}$. If the object is placed $30\text{ cm}$ away from the lens, where is the image formed? Calculate its magnification.

25.

Two thin lenses of power $+5.0\text{ D}$ and $-2.5\text{ D}$ are in contact. Find the equivalent focal length of the combination.

26.

Draw a ray diagram to show the formation of a real, inverted, and magnified image by a convex lens. State the position of the object.

AI Prompt: Create a mathematically correct physics ray diagram showing a convex lens forming a real, inverted, magnified image. Object placed between F and 2F. Fully white background, landscape mode.

File Name: Level1_Q26_ConvexLensRealMag.png

27.

A convex lens of focal length $10\text{ cm}$ is placed at a distance of $12\text{ cm}$ from a wall. How far from the lens should an object be placed so as to form its real image on the wall?

28.

A convex lens made of material of refractive index $1.5$ has a focal length of $20\text{ cm}$ in air. Find its focal length when it is completely immersed in water of refractive index $1.33$ ($4/3$).

29.

An object $5\text{ cm}$ high is held $25\text{ cm}$ away from a converging lens of focal length $10\text{ cm}$. Find the position, size, and nature of the image formed.

30.

What happens to the focal length of a convex lens if it is cut into two equal halves (a) vertically along its principal axis, and (b) horizontally perpendicular to its principal axis?

31.

A concave lens of focal length $15\text{ cm}$ forms an image $10\text{ cm}$ from the lens. How far is the object placed from the lens?

Topic 4: Prism & Dispersion

32.

Draw a ray diagram showing the refraction of light through a glass prism. Clearly mark the angle of incidence ($i$), angle of emergence ($e$), angle of prism ($A$), and angle of deviation ($\delta$).

AI Prompt: Create a mathematically correct physics ray diagram showing monochromatic light refracting through a triangular glass prism. Mark angle of incidence (i), emergence (e), prism angle (A), and deviation angle (delta). Fully white background, landscape mode.

File Name: Level1_Q32_PrismRefraction.png

33.

A ray of light passes through an equilateral glass prism such that the angle of incidence is equal to the angle of emergence. If the angle of emergence is $3/4$ times the angle of the prism, calculate the angle of deviation.

34.

Define dispersion of white light. Why do different colors deviate through different angles on passing through a prism?

35.

Plot a graph showing the variation of the angle of deviation ($\delta$) with the angle of incidence ($i$) for a glass prism. Mark the position of minimum deviation ($\delta_m$).

AI Prompt: Create a mathematically correct physics graph plotting angle of deviation (delta) vs angle of incidence (i) for a glass prism. U-shaped curve, marking minimum deviation (delta_m). Fully white background, landscape mode.

File Name: Level1_Q35_PrismDeviationGraph.png

36.

An equilateral glass prism has a refractive index of $1.5$. Calculate the angle of minimum deviation. ($\sin 48.6^\circ = 0.75$)

37.

A thin prism of refracting angle $5^\circ$ gives a deviation of $3.2^\circ$. What is the refractive index of the material of the prism?

38.

For a glass prism, the angle of minimum deviation is equal to the angle of the prism. Find the refractive index of the glass.

39.

Draw a ray diagram illustrating the dispersion of a narrow beam of white light into its constituent colors by a glass prism.

AI Prompt: Create a mathematically correct physics ray diagram showing dispersion of white light through a triangular glass prism. Splitting into spectrum (Red top, Violet bottom). Fully white background, landscape mode.

File Name: Level1_Q39_PrismDispersion.png

40.

Why does a rectangular glass slab not show dispersion, whereas a prism does?

Topic 5: Optical Instruments

41.

Draw a labelled ray diagram for a compound microscope when the final image is formed at the least distance of distinct vision ($D$).

AI Prompt: Create a mathematically correct physics ray diagram of a compound microscope. Objective lens forming real inverted image, eyepiece forming highly magnified virtual final image at distance D. Fully white background, landscape mode.

File Name: Level1_Q41_CompoundMicroscope.png

42.

Write the formula for the magnifying power of a compound microscope (final image at D). Why must the focal lengths of both lenses be small?

43.

An astronomical telescope has an objective of focal length $144\text{ cm}$ and an eyepiece of focal length $6.0\text{ cm}$. Calculate its magnifying power and tube length in normal adjustment.

44.

State two main advantages of a reflecting type telescope over a refracting type telescope.

45.

Draw a neat labelled ray diagram of a Cassegrain reflecting telescope.

AI Prompt: Create a mathematically correct physics ray diagram of a Cassegrain reflecting telescope. Show primary parabolic mirror, secondary convex mirror, light reflecting through central hole to eyepiece. Fully white background, landscape mode.

File Name: Level1_Q45_CassegrainTelescope.png

46.

A simple microscope has a magnifying power of 6 when the image is formed at the least distance of distinct vision ($25\text{ cm}$). Find the focal length of the lens.

47.

A compound microscope has an objective of focal length $1.25\text{ cm}$ and an eyepiece of focal length $5\text{ cm}$. An object is placed at $1.5\text{ cm}$ from the objective. If the final image is at infinity, calculate the magnifying power.

48.

For the astronomical telescope in Question 43, what would be the magnifying power if the final image is formed at the least distance of distinct vision ($25\text{ cm}$)?

49.

Why is the objective of a telescope made of a large aperture, while the objective of a microscope is made of a very small aperture?

50.

Draw a ray diagram of an astronomical telescope when the final image is formed at infinity.

AI Prompt: Create a mathematically correct physics ray diagram of an Astronomical Telescope in normal adjustment (image at infinity). Large objective, small eyepiece, parallel incident rays exiting parallel. Fully white background, landscape mode.

File Name: Level1_Q50_AstronomicalTelescope.png

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