Question

When an object is placed at a distance of 40 cm from a concave spherical mirror the magnification produced is 1/2 where shouldtge object be placed to get a magnification of 1/3?

Answer 1

Hey mate answer above

Answer 2

Answer: The object is placed at 80 cm from the mirror.

Explanation:

Given that,

The distance of the object u = -40 cm

Magnification $m = \dfrac{1}{2}$

We know that,

The magnification is

$m = -\dfrac{v}{u}$

$\dfrac{1}{2}=\dfrac{-v}{-40}$

$v = 20 cm$

The focal length is

$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$

$\dfrac{1}{f}=\dfrac{1}{20}+\dfrac{1}{-40}$

$\dfrac{1}{f}= \dfrac{1}{40}$

$f = 40 cm$

When the magnification is $\dfrac{1}{3}$

$m = -\dfrac{v}{u}$

$\dfrac{1}{3}=-\dfrac{v}{u}$

$v = -\dfrac{3}{u}$

Now, using mirror's formula

$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$

$\dfrac{1}{40}=\dfrac{-3}{u}+\dfrac{1}{u}$

$\dfrac{1}{40}=\dfrac{-2}{u}$

$u = -80 cm$

Hence, The object is placed at 80 cm from the mirror.