An object is located at a distance of 105 cm from a concave mirror of focal leng

Question

An object is located at a distance of 105 cm from a concave mirror of focal length 24.5 cm. Another concave mirror of focal length 7.01 cm is located 24.5 cm in front of the first concave mirror. The reflecting sides of the two mirrors face each other. Assume the second mirror is partially silvered so that the light rays from the object go through it, reflect from the first mirror, and then reflect from the second mirror.

a) What is the location of the final image formed by the two mirrors? Give your answer in terms of the distance from the second mirror.

b) What is the total magnification by the combination?

Explanation / Answer

a) for first mirror
object distance u = -105 cm
focal length, f = -24.5
let image distance be v
according to mirror formula
(1/v) + (1/u) = 1/f
1/v - 1/105 = - 1/ (24.5)
v = -31.95 cm
i.e image is formed 31.95cm on the left of the first concave mirror.
image formed by first mirror is object for the second mirror
for second mirror
object distance p = 31.95 - 24.5
= 7.45cm
focal length = - 7.01
let image distance be q
1/p + 1/q = 1/f
1/ 7.45 + 1/ q = -1/ 7.01
q = - 3.611
image is formed on the right of second mirror and left of first mirror
b)
for first mirror

m = -0.304

for second mirror

m = -q/p = 0.4846

total magnification = -0.304*0.4846 = 0.1473

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