Question

The incident ray and reflected ray from the mirror are at right angle to each other. What is the angle of incidence?

Answer 1

Step 1: Given:

The incident ray and reflected ray are at the right angle.

$$\begin{gathered} i.e.,angleofincidence+angleofreflection={90}^o \\ \overbrace{i}+\stackrel{⏜}{r}={90}^o \end{gathered}$$

Step 2: Formula used:

First law of reflection states that angle of incidence is equal to angle of reflection

$\stackrel{⏜}{i}=\stackrel{⏜}{r}$

Step 3: Calculation:

$$\begin{gathered} Wehave, \\ \stackrel{⏜}{i}+\stackrel{⏜}{r}={90}^o \\ But\stackrel{⏜}{i}=\stackrel{⏜}{r} \\ therefore,2\times \stackrel{⏜}{i}={90}^o \\ \stackrel{⏜}{i}=\frac{{90}^o}{2} \\ \stackrel{⏜}{i}={45}^o \end{gathered}$$

Hence, the angle of incidence is 45^o .