Question

Calculate the number of images formed by two plane mirrors kept at an angle of ${30}^{\circ },{72}^{\circ }and{90}^{\circ }$ respectively. (Assume the object is placed symmetrically with respect to both the mirrors in all the three cases)

• A. 11, 5 & 4
  
• B. 11,4 & 5
  
• C. 12, 4 & 4
  
• D. 11, 4 & 3
  

Answer 1

The correct option is D 11, 4 & 3

We have a formula for the number of images formed given the inclination between the two plane mirrors.
In the first case;
$\frac{360}{\theta }=\frac{360}{30}=12.\left(Anevennumber\right).$
So,
The number of images formed =12-1=11.
In the second case;
$\frac{360}{\theta }=\frac{360}{72}=5.(Anoddnumber,symmetricallyplaced).$
So, the number of images formed = 5-1=4.
In the third case,
$\frac{360}{\theta }=\frac{360}{90}=4.\left(Anevennumber\right).$
So, the number of images formed 4-1=3.