Question

A converging lens and a concave mirror are placed a distance D = 133 cm apart. The lens is placed such that it is to the left of the refelcting side of the mirror. The lens has focal length f1 = 5 cm, and the mirror has focal length f2 = 6 cm. If an object is placed a distance of do = 35 cm to the left of the lens, what is the image distance in centimeters from the lens? Round your answer to two decimal places.

Answer 1

object distance for the first lens,

u1 = 35 cm

let v1 is the image distance.

use, 1/u1 + 1/v1 = 1/f1

1/v1 = 1/f1 - 1/u1

1/v1 = 1/5 - 1/35

v1 = 5.83 cm

This image acts as object for the mirror.

object distance for the mirror, u2 = 133 - 5.83

= 127.17 cm

f2 = 6 cm

let v2 is the object distance for the mirror.

use,1/u2 + 1/v2 = 1/f2

1/v2 = 1/f2 - 1/u2

1/v2 = 1/6 - 1/127.17

v2 = 6.30 cm

This image again acts as object for the lens.

so, object distance, u3 = 133 - 6.30 = 126.7 cm

let v3 is the image distance.

use,

1/u3 + 1/v3 = 1/f1

1/v3 = 1/f1 - 1/u3

1/v3 = 1/5 - 1/126.7

v3 = 5.21 cm <<<<<<<<<---------Answer

The final image is 5.21 cm from the lens in the left side.