An object O is placed in front of a small plane mirror `M_(1)` and a large convex mirror `M_(2)` of focal length `f`. The distance between O and `M_(1)` is x, and the distance between `M_(1)` and `M_(2)` is y. The images of O forned by `M_(1)` and `M_(2)` coincide. The magnitude of f is

Options

A. x-y
B. `(x^(2)-y^(2))/(2y)`
C. `x^(2) + y^(2))/(2y)`
D. `(x^(2) + y^(2))/(x+y)`

Answer

B

Explanation

Let .v. be the image of convex mirror
`because ` dor plane mirror
Object distance = Image distance
x = y + v implies v = x - y
`:.` . For convex mirror u = x + y, v = x — y
Then`1/f=1/v+1/u`