Question

The figure shows light reflecting from two perpendicular reflecting surfaces AB. Find the angle between the incoming$\mathbf{\text{ray}}\mathbf{}\mathit{i}$and the outgoing$\mathbf{\text{ray}}\mathbf{}\mathit{r}\mathbf{\text{'}}$.

Figure:

Short answer

The angle between them is $\text{180°}$.

Step-by-step solution

Determining the concept

The angle of incidence is equal to the angle of reflection. Using this concept, the angle between the incoming ray and outgoing ray after the reflection from the mirrors can be found.

The formula is as follows:

The angle of incidence = Angle of reflection

Determinethe angle between the incoming ray i and the outgoingray r' .

${\theta }_5={\theta }_6$

From the above diagram,

${\theta }_1={\theta }_2$ …… (1)

Since the bottom mirror and normal 1 are parallel, it implies that

${\theta }_2={\theta }_5$ …… (2)

Using the law of reflection, it can be written,

${\theta }_3={\theta }_4$ …… (3)

Also,

From simple geometry,

${\theta }_3+{\theta }_5={\theta }_4+{\theta }_6=90$ …… (4)

From equations (3) and (4), it can be concluded that,

${\theta }_5={\theta }_6$ …… (5)

Now from equations (1), (2), and (5) the required angle is:

${\theta }_1={\theta }_6$

This implies that the incident ray and reflected ray are parallel to each other, but their direction is opposite to each other.

Therefore, the angle between them is$\text{180°}$