Question

An object is 15.4 cm in front of a thin converging lens that has a focal length equal to 10.0 cm. A concave mirror that has a radius equal to 10.0 cm is 26.2 cm in back of the lens.

(a) Find the position of the final image formed by the mirror-lens combination.
cm from the lens, on the same side as the original object.

Please solve the Q

Answer 1

for the lens,
u1 = 15.4 cm
f1 = 10 cm
let v1 is the image distance for the lens.

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

1/v1 = 1/f1 - 1/u1

1/v1 = 1/10 - 1/15.4

v1 = 28.5 cm

object distancce for the mirror, u2 = -28.5 + 26.2

= -2.3 cm
f2 = -R/2 = -10/2 = -5.0 cm

let v2 is the image distance for the mirror.

let 1/v2 + 1/u2 = 1/f2

1/v2 = 1/f2 - 1/u2

1/v2 = 1/(-5) - 1/(-2.3)

v2 = 4.26 cm

This image acts as object for the lens.

for the lens, object distance, u3 = 26.2 - 4.26 = 21.94 cm

let v3 is the image distance

1/u3 + 1/v3 = 1/f

1/v3 = 1/f - 1/u3

1/v3 = 1/10 - 1/21.94

v3 = 18.4 cm

so, the final image is 18.4 cm infront of the lens. <<<<<<<<<<--------Answer