An incident ray is 8.00 cm away from, and parallel to, the principal axis of a p

Question

An incident ray is 8.00 cm away from, and parallel to, the principal axis of a plano-convex lens, whose convex surface has a radius of 20.0 cm, as shown below. Assume that the index of refraction of the lens material is 1.50. (10) How far from the vertex does the refracted ray cross the principal axis? (A) 32.2cm; (B) 34.2cm; (C) 36.2cm; (D) 38.2cm; (E) 40.2cm. (11) What is the focal length if the lens is treated as a thin lens? (A) 34.3cm; (B) 36.2 cm; (C) 38.1cm; (D) 40.0 cm; (E) 41.9 cm. (12) What is the answer to the last question if the convex surface is replaced with a concave surface of the same radius? (A) -41.9cm; (B) -40.0 cm; (C) -38.1cm; (D) -36.2 cm; (E) -34.3 cm.

Explanation / Answer

given

object distance, u = 8 cm

R1 = infinite

R2 = -20 cm

n = 1.5

10) E) 40.2 cm

the rays crosses the pricipal axis at focal point.

use Len's maker's equation,

1/f = (n-1)*(1/R1 - 1/R2)

1/f = (1.5 - 1)*(1/infinite - 1/(-20))

1/f = 0.5/20

f = 40 cm

11) D) 40 cm

12) B) -40 cm

1/f = (n-1)*(1/R1 - 1/R2)

1/f = (1.5 - 1)*(1/infinite - 1/(20))

1/f = 0.5/(-20)

f = -40 cm

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