Question

Two plane mirrors at an angle such that a ray incident on a mirror undergoes a total deviation of ${240}^{\circ }$ after two reflections.

• A. the angle between the mirrors is ${60}^{\circ }$
• B. the number of images formed by this system will be 5 , if an object is placed symmetrically between the mirrors.
• C. the no. of images will be 6 if an object is kept unsymmetrically between the mirrors.
• D. a ray will retrace its path after 2 successive reflections, if the angle of incidence on one mirror is ${60}^{\circ }$ .

Answer 1

The correct option is A the angle between the mirrors is ${60}^{\circ }$

$\begin{array}{c}i=\text{angle of incidence on}\\ \text{first mirror}\\ \alpha =\text{angle of incidence}\\ \text{on second mirror}\end{array}$

$f_1+d_2={240}^{\circ }[$ as the total devition

should be ${240}^{\circ }]$

$Q=\frac{\pi -{90}^{\circ }-{90}^{\circ }+i+\alpha =i+\alpha }{\text{sun of ongles of a triangle}}$-(1)

$f_{\text{Total}}={360}^{\circ }-2i-2dx={240}^{\circ }$

By considering both points of

reflection

$i+\alpha ={60}^{\circ }$

By (4) we proved that $i+\alpha =\theta ={60}^{\circ }J$ i.e angle between

mirrors. Hence option ' $A$ ' is correct.