Chapter 17, Problem 40A

(a)

To determine

The angle at which the light ray is reflected from the other mirror.

Answer to Problem 40A

The angle at which the light ray is reflected from the other mirror is $60°$ .

Explanation of Solution

Given:

The given diagram is shown below:

  

The angle between the two mirror is $90°$.

The angle of incident is $30°$.

Calculation:

According to the law of reflection, the angle made by the reflected ray measured from the normal to a reflecting surface is equal to the angle made by the incident ray measured from the same normal.

Using this information, the sketch of incident and reflected rays of the two mirrors is shown below:

  

Now, let’s find the angle of incidence of the second mirror. In the figure, one can easily see that the reflected ray of the first mirror is the incident ray of the other.

Consider the quadrilateral formed by the sides of the mirrors and the two normal lines. The angle made by the two normal lines will be equal to $90°$ .

  

Now, consider the triangle that is formed by two normal lines and the reflected ray of the first mirror. Since the sum of angle of the triangle is $180°$ , we can say that the angle of the incident ray of the second mirror with the normal is $60°$ . By the law of reflection, the reflected ray will also make an angle of $60°$ with its normal.

Conclusion:

Hence, the angle at which the light ray is reflected from the other mirror is $60°$ .

(b)

To determine

To draw: The diagram in which the reflected light rays to show that this mirror system acts as a retro reflector.

Explanation of Solution

Given:

The given diagram is shown below:

  

The angle between the two mirror is $90°$.

The angle of incident is $30°$.

Calculation:

In a retro reflector, the reflected ray follows the same direction and the path as the incident ray. Put two arrows each in the opposite on the same ray to show the incident and the reflected rays in the mirror system that acts as the retro reflector.

The diagram is shown below: