Question

Find the number of imges formed according to the given cases

• A. $8,9$
• B. $9,8$
• C. $8,8$
• D. $9,9$

Answer 1

The correct option is A $8,9$

If the image of an object is viewed in two plane mirrors that are inclined to each other, more than one image is formed. The number of images formed depends on the angle between the two mirrors and the position of the object in between the mirrors.

Case -I:
Mirrors are at angle of ${40}^{\circ }$ with each other and object is placed along the angular bisector.

To find the number of images formed by the system of mirrors,

we find ,$\frac{{360}^{\circ }}{\theta }=\frac{{360}^{\circ }}{{40}^{\circ }}=9$ (odd number)

$\therefore$ Number of images $=(\frac{{360}^{\circ }}{\theta }-1)=9-1=8$

Case -II:

Mirrors are at angle of ${40}^{\circ }$ with each other and object is not placed along the angular bisector.

To find the number of images formed by the system of mirrors,

we find ,$\frac{360}{\theta }=\frac{360}{40}=9$ (odd number)

$\therefore$ Number of images $=\left(\frac{360}{\theta }\right)=9$

Hence, option (a) is the correct answer.

Note:- If $\frac{360}{\theta }$ is an odd number, student is advised to verify if the object is placed on the angular bisector or not.