Question

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Good Morning ^_^ !

Question-
Find the position of final image after 3 successive reflections taking first reflection on M1.

Please refer the above attachment for the diagram..

Thanks in advance :D​

Answer 1

The position of final image after 3 successive reflections is 5.5 cm.

Explanation:

The lens formula is given as:

1/f = 1/u + 1/v

Where,

f = Focal length

u = Object distance

v = Image distance

Now, the radius of curvature (R) and focal length is given as:

f = R/2 = 20/2 = 10 cm

Focal length of concave lens = -10 cm

First reflection:

f = -10 cm and u = - 15 cm

On substituting the values on lens formula, we get,

-1/10 = -1/15 + 1/v

1/v = -1/10 + 2/15 ⇒ 1/v = 1/30

∴ v = 30 cm

Second reflection: (reflection is from concave mirror)

f = 20/2 = 10 cm and u = 55 cm

1/10 = 1/55 + 1/v

1/v = 1/10 - 1/55 ⇒ 1/v = 9/110

∴ v = 110/9 = 12.2 cm

Third reflection: (reflection is from convex mirror)

f = 10 cm and u = -12.2 cm

1/10 = -1/12.2 + 1/v

1/v = 1/10 + 1/12.2 ⇒ 1/v = 111/610

∴ v = 610/111 = 5.5 cm