A convex mirror of focal length f forms an image which is (1/n) times the object. The distance of the object from the mirror is

Question

A convex mirror of focal length f forms an image which is (1/n) times the object. The distance of the object from the mirror is (A)  ( (n-1/n) )f  (B)  ( (n+1/n) )f  (C)  (n+1)f  (D)  (n-1)f

Tardigrade Admin · Accepted Answer

Given magnification, m=(1/n) So, (1/n)=-(v/u) or v=-(u/n) By using mirror formula, (1/f)=(1/v)+(1/u) =(1/-u/n)+(1/u) ⇒ u=-(n-1)f

Q. A convex mirror of focal length $f$ forms an image which is $\frac{1}{n}$ times the object. The distance of the object from the mirror is

$(\frac{n - 1}{n}) f$

$(\frac{n + 1}{n}) f$

$(n + 1) f$

$(n - 1) f$

Given magnification,
$m = \frac{1}{n}$
So, $\frac{1}{n} = - \frac{v}{u}$
or $v = - \frac{u}{n}$
By using mirror formula,
$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
$= \frac{1}{- u / n} + \frac{1}{u}$
$\Rightarrow$ $u = - (n - 1) f$

Q. A convex mirror of focal length f forms an image which is n1​ times the object. The distance of the object from the mirror is

(nn−1​)f

(nn+1​)f

(n+1)f

(n−1)f