Question

A mirror forms an image which is 30 cm from an object and twice its height.

(a) Where must the mirror be situated?

(b) What is the radius of curvature?

(c) Is the mirror convex or concave?

Answer 1

Given Data:

Distance between object and image, $v-u=30cm$

Magnification,

$m=+2=\frac{-v}{u}$

$v=-2u$

Step 1: To find Distance of an object;

$v-u=\mathrm{30.....}\left(1\right)$

$v=-2u.....\left(2\right)$

From eq(1) and (2):

$-2u-u=30⟹-3u=30cm$

$u=-10cm$

Mirror is situated at a distance of 10cm from object.

Step 2: Radius of curvature of mirror:

Given Data:

$u=-10cm$

$v=-2(-10)=20cm$

From mirror formula,

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

$\frac{1}{f}=\frac{1}{20}+\frac{1}{-10}$

$\frac{1}{f}=\frac{1-2}{20}⟹f=-20cm$

And radius of curvature will be double of focal length of mirror,

$R=2f$

$R=2\times (-20)=-40cm$

Radius of curvature =$\text{- 40cm}$

(c)Concave mirror (since sign of focus is negative)