Question

A plane mirror is placed on an inclined plane of inclination ${30}^{\circ }$. An incident ray falling perpendicular to inclined plane gets reflected as shown. What is the value of angle of reflection '$\text{x}$'?

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is A ${30}^{\circ }$

According to the laws of reflection, angle of incidence is equal to angle of reflection. This law is valid irrespective of the orientation of the reflecting surface.
Given that,
Angle of inclination = ${30}^{\circ }$
Let's draw a perpendicular line on the base and name angle formed as '$\text{z}$'.


We know that, corresponding angles are equal if the transversal intersects two parallel lines.$\angle z=\angle y$
So,
$\text{y}+{30}^{\circ }$ = ${90}^{\circ }$
$\text{y}={60}^{\circ }$
Angle of incidence $={90}^{\circ }-{60}^{\circ }={30}^{\circ }$
Using the law,
Angle of incidence is equal to angle of reflection.
Hence,
Angle of reflection, $\text{x}$ = ${30}^{\circ }$