Question

If the light strikes the first mirror at anangle θ1, what is the reflected angle θ2?

Answer 1

Concepts and reason

The concept used to solve this problem is the basic geometric properties of triangle and Laws of reflection.

Use the basic geometric properties of triangle and Laws of reflection to obtain the required angle made by the light ray.

Fundamentals

The laws of Reflection.

1. The normal ray and the reflected ray should be in the same plane.

2. The ray of light only reflected through mirror surface and water surface.

3. When a light ray strike on a mirror surface, then the incident angle of the light and reflected angle of the light is equal.

The basic geometric properties of triangle are as follows:

• The sum of the angles in a triangle is $180^\circ$ .

• The sum of the length of any two sides of a triangle is greater than the length of the third side.

The reflected ray diagram is as follows:

Figure (1)

From figure (1), the angle between the strike’s ray to the normal line on first mirror and the angle between the reflected ray to the normal line are equal. Hence, ${\theta _1} = {\theta _2}$ . The angle on second mirror when the reflected ray again strikes on the second mirror, the angle between the reflected ray which is coming to reflect on the second mirror to the normal on second mirror is ${\theta _3}$ and the angle between reflected ray on second mirror to the normal line is ${\theta _6}$ . The angle between the reflected ray on first mirror to the second mirror is ${\theta _4}$ .

Angle ${\theta _3}$ from the simple geometry property is as follows:

${\theta _3} = 90^\circ - {\theta _2}$

Angle ${\theta _4}$ from the properties of triangle is as follows:

${\theta _4} = 180^\circ - \alpha - \left( {90 - {\theta _1}} \right)$

The angle of reflected ray to the normal line and the angle between the strike ray to the normal on the second mirror is equal as shown below:

${\theta _5} = 90^\circ - \left( {180^\circ - \alpha - \left( {90 - {\theta _1}} \right)} \right)$

Angle ${\theta _2}$ is as follows:

${\theta _1} = {\theta _2}$

Ans:

The reflected angle is same as the incident angle.