Ray Optics & Optical Instruments

A boy of height 1.7 m, with his eyes 1.6 m above the floor, stands in front of a plane mirror fixed on a wall. What is the minimum length of the mirror required for him to see his complete image?

Two plane mirrors are inclined to each other at 60°, with a point object placed exactly on the bisector between them. How many images are formed?

A man walks directly towards a stationary plane mirror at a speed of 3 m/s. At what rate does the distance between the man and his image decrease?

An object is placed 30 cm in front of a concave mirror of focal length 20 cm. Find the position and nature of the image.

An object is placed 30 cm in front of a convex mirror of focal length 15 cm. Find the position and nature of the image.

For a spherical mirror of focal length 15 cm, the image of an object is formed at a distance of 5 cm from the focus (measured from the focus, on the object side). Using Newton's formula, find the distance of the image from the focus on the other side.

A ray of light travelling in air is incident on a water surface (μ_water = 4/3) at an angle of incidence of 53° (sin 53° = 0.8). What is the angle of refraction?

A tank is filled with a liquid of refractive index 1.5 to a depth of 12 cm. What is the apparent depth of an object lying at the bottom, when viewed from directly above?

A glass slab of thickness 6 cm and refractive index 1.5 is placed over a printed page. By how much does the page appear to be shifted (towards the slab)?

Find the critical angle for a glass–air interface if the refractive index of the glass is √2.

Taking the refractive index of diamond to be 2.5, what is the speed of light inside a diamond? (c = 3 × 10⁸ m/s)

A point object is placed in air at a distance of 40 cm from the pole of a convex spherical glass surface (R = 20 cm, μ_glass = 1.5). Where is the image formed?

An equiconvex lens has both radii of curvature equal to 20 cm and is made of glass of refractive index 1.5. What is its focal length?

An object is placed 15 cm in front of a convex lens of focal length 10 cm. Find the position and magnification of the image.

An object is placed 30 cm in front of a concave lens of focal length 20 cm. Find the position and magnification of the image.

A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 25 cm. What is the focal length of the combination?

An equilateral glass prism (A = 60°) has a refractive index of 1.5. What is the angle of minimum deviation? (Use sin 48.6° ≈ 0.75)

An astronomical telescope has an objective of focal length 100 cm and an eyepiece of focal length 5 cm. What is its magnifying power when the final image is formed at infinity?