Question

An object is placed 18 cm in front of a spherical mirror. If the image is formed at 4 cm to the right of the mirror then calculate its focal length. Is the mirror concave or convex. What is the nature of the image. What is the radius of curvature?

Answer 1

Step 1: Given Data

Since the image is formed at right side so it is a virtual and erect image. Generally, convex mirror forms virtual and erect image. So it is a convex mirror.

Object distance $u=-18cm$

Image distance, $v=4cm$

Step 2: Calculation of focal length

According to the mirror formula,

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

$\frac{1}{f}=\frac{1}{4}+\frac{1}{-18}$

$\frac{1}{f}=\frac{9-2}{36}$

$f=\frac{36}{7}$

$f=5.1cm$

The radius of curvature is $2f$=2$\times$ $5.1=10.2cm$

Focal lenght$=5.1cm$ and radius of curvature$=10.2cm$