Question

A concave spherical mirror, forms a 40 cm high real image of an object, whose height is 10 cm. The radius of the mirror is 60 cm. Find the distance from the object to its image.

• A. 97.5 cm
• B. 75 cm
• C. 90cm
• D. 187.5 cm

Answer 1

The correct option is D 187.5 cm

$\begin{array}{c}\text{I =height of image}\\ O=\text{height of object}\\ v=\text{distance of}\text{image}\\ u=\text{distance of}\text{object}\\ R=\text{radius}\\ R=2f\text{knowm}\end{array}$

$\text{Magnification}=-\frac{v}{u}=\frac{I}{O}$

$\begin{array}{c}I=40cm\\ O=10cm\\ R=60cm\\ \Rightarrow f=30cm\\ \frac{40}{10}=-\frac{v}{u}\\ 4u=-v\\ \frac{1}{v}-\frac{1}{u}=\frac{1}{f}\end{array}$

$-\frac{1}{4u}-\frac{1}{u}=\frac{1}{30}$

$\begin{array}{c}-5=\frac{4u}{30}\\ -\frac{150}{4}=u\\ -37.5m=u\\ \nu =-4u\\ =-150cm\end{array}$

$\begin{array}{c}\text{Distance between object}\text{and image}\\ \begin{array}{cc}\Rightarrow v+u& =-150-37.5\\ & =-187.5cm\end{array}\end{array}$