Ray Optics and Optical Instruments — Practice

Question 1

An object is placed 20 cm in front of a concave mirror of focal length 10 cm. Find the image distance and state its nature.

Accepted Answer

Apply 1/v + 1/u = 1/f with f negative for a concave mirror, then read the sign of v. Answer: v = -20 cm; real, inverted, same size.

Question 2

Find the critical angle for a glass-air interface if the refractive index of glass is 1.5.

Accepted Answer

Use sin C = 1/n, since light must travel from the denser to the rarer medium. Answer: C = 41.8 degrees.

Question 3

A convex lens of focal length 25 cm is placed in contact with a concave lens of focal length 50 cm. Find the power of the combination.

Accepted Answer

Convert each focal length to a power in dioptres and add them. Answer: P = +2 D, so the combination converges.

Question 4

A double convex lens of refractive index 1.5 has both radii equal to 20 cm. Find its focal length.

Accepted Answer

Use the lens maker's formula, remembering that the two radii carry opposite signs. Answer: f = 20 cm.

Question 5

A coin lies at the bottom of a vessel containing 16 cm of a liquid of refractive index 1.6. Find its apparent depth and the apparent shift.

Accepted Answer

Divide the real depth by the refractive index, then take the difference. Answer: Apparent depth 10 cm; shift 6 cm.

Question 6

A prism of refracting angle 60 degrees gives a minimum deviation of 30 degrees. Find the refractive index of its material.

Accepted Answer

Apply the minimum deviation formula, where the path through the prism is symmetric. Answer: n = 1.414.

Question 7

A magnifying glass has focal length 5 cm. Find its magnifying power when the image is formed at infinity and when it is formed at the near point.

Accepted Answer

The two settings give D/f and 1 + D/f respectively, with D = 25 cm. Answer: 5 at infinity; 6 at the near point.

Question 8

A compound microscope has an objective of focal length 1.0 cm and an eyepiece of focal length 5.0 cm. The object is 1.1 cm from the objective and the final image is at 25 cm. Find the magnifying power.

Accepted Answer

Find the objective's image distance first, then multiply its linear magnification by the eyepiece's angular magnification. Answer: M = 66.

Question 9

A telescope has an objective of focal length 100 cm and an eyepiece of focal length 4.0 cm. Find its magnifying power in normal adjustment and the tube length.

Accepted Answer

Normal adjustment gives the plain ratio of focal lengths, and the tube length is their sum. Answer: M = 25; tube length 104 cm.

Question 10

Show, using the mirror equation, that a convex mirror always forms a virtual image that is diminished and lies between the pole and the focus.

Accepted Answer

Rearrange to v = f|u|/(f + |u|) and examine the sign and size of v and of m for every object position. Answer: v is positive and less than f, and m = f/(f + |u|) is always below 1.

Practice — Ray Optics and Optical Instruments

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