Question

mafnification produced by a convex mirror is 1/n. If the focal length is f, find the image distance ,object distance in terms of curvature r​

Answer 1

Answer:

u = (1-n)r/2

v = (1-n)r/2n

Explanation:

m = + 1/n

focal length = -f

v = ?

u = ?

m = -v/u = + 1/n

or u = -vn  ------------(I)

Using mirror formula

1/focal length = 1/v + 1/u

or -1/f = 1/v - 1/vn

or -1/f = (n-1)/(vn)

or 1/f = (1-n)/vn

or vn = (1-n)f  ------------(II)

or v = (1-n)f/n

Replacing f by r/2, we get

v = (1-n)r/2n

From eqn. I and II,

we get

u = (1-n)f

Again replacing f by r/2, we get

u = (1-n)r/2