Question

four identical thin lenses are kept on beside the other on the same optical Axis as shown in the figure the right surface of right most lens is silvered focal length of each lens is 20 cm and radius of the Silver the surface is 20cm the focal length of the combined systems

Answer 1

Answer: -2 cm

Explanation: first of all find the equivalent focal length of all the four lenses (ignore the silvering..take it as a normal lens)

1/f(eq) = 1/f1 + 1/f2 + 1/f3 + 1/f4

Now all the focal lengths are same so we can directly write it as 4/f

F = 20 cm...and 4/20 = 5cm

Now for combined system of mirror and lens we have formula

2/f(lens) + 1/f(mirror) = 1/f(eq)

Now put f(lens) = 5cm

f(mirror) = 10cm

And you will get f(eq) = 2cm

....dont forget to put negative sogn before 2..

I hope this will help you!!! :)