Question

An image of an object obtained by a convex mirror is n times smaller than the object. If the focal length of lens is f, the object distance would be _______ . (A) f/n
(B) f/(n-1)
(C) (n — 1)f
(D) nf

Answer 1

Answer:

(1-n)f

Explanation:

Given, the image of an object obtained by a convex mirror is n times smaller than the object and the focal length of the mirror is f.

Assuming,

$h_i$ = height of the image.

$h_o$ = height of the object.

Therefore, $h_o = nh_i$.

The magnification of the mirror is given by

$m=\dfrac{h_i}{h_o} = \dfrac{h_i}{nh_i}=\dfrac 1n.$

The magnification of the mirror is also defined in terms of object distance $u$ and image distance $v$ from the mirror as

$m=\dfrac{-v}{u}\\\\\therefore \dfrac{-v}{u}=\dfrac 1n\\\Rightarrow v=-\dfrac un.$

According to the mirror equation,

$\dfrac 1f = \dfrac 1v+\dfrac 1u$.

Putting the value of $v$,

$\dfrac 1f = -\dfrac nu+\dfrac 1u=\dfrac{-n+1}{u}\\\Rightarrow u=(1-n)f.$