Question

Two plane mirrors are placed making an angle $\theta$ in between them. What is the expression for the number of images formed of an object placed in between the mirrors?

• A. $n$ if $n=\frac{{360}^{\circ }}{{\theta }^{\circ }}$ is odd and object is asymmetrically placed
• B. $n-1$ if $n=\frac{{360}^{\circ }}{{\theta }^{\circ }}$ is even, or odd and object is symmetrically placed.
• C. Both A & B
• D. None

Answer 1

The correct option is C Both A & B

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 depends on the angle between the two mirrors.
The number of images formed in two plane mirrors inclined at an angle A to each other is given by the below formula.
Number of images $n=\frac{360}{A}-1$
The number of images formed $n=\frac{360}{A}-1$, if $\frac{360}{A}$ is an even integer.
If $\frac{360}{A}$ is odd integer, the number of images formed $n=\frac{360}{A}-1$ when the object is kept symmetrically, and $n=\frac{360}{A}$ when object is kept asymmetrically.
If $\frac{360}{A}$ is a fraction, the number of images formed is equal to its integral part.
As the angle gets smaller (down to 0 degrees when the mirrors are facing each other and parallel) the smaller the angle the greater the number of images.