Problem: Two plane mirrors are inclined at an angle of 140 degree to each other. A ray of light incident on either mirror at an angle of incidence is 20 degree is double reflected. The two mirrors deviate the incident ray through an angle?

Solution:

To solve the problem, we need to follow the steps given below:

Step 1: Draw a diagram

We start by drawing a diagram that represents the problem. We have two plane mirrors inclined at an angle of 140 degrees, and a ray of light that is incident on one of the mirrors at an angle of 20 degrees. We need to find the angle through which the two mirrors deviate the incident ray.

Step 2: Find the angle of reflection

The first reflection occurs when the incident ray strikes the first mirror. According to the law of reflection, the angle of incidence is equal to the angle of reflection. Therefore, the angle of reflection is also 20 degrees.

Step 3: Find the angle of incidence for the second reflection

The angle of incidence for the second reflection is the angle between the reflected ray and the normal to the second mirror. We can use the fact that the sum of the angles in a triangle is 180 degrees to find this angle. The angle between the reflected ray and the normal is (180 - 140)/2 = 20 degrees.

Step 4: Find the angle of reflection for the second reflection

Using the law of reflection again, we can find the angle of reflection for the second reflection. The angle of reflection is also 20 degrees.

Step 5: Find the angle through which the two mirrors deviate the incident ray

The angle through which the two mirrors deviate the incident ray is the sum of the angles between the incident ray and the two reflected rays. We can find this angle by subtracting the angle of incidence from the sum of the angles of reflection. Therefore, the angle through which the two mirrors deviate the incident ray is (20 + 20) - 20 = 20 degrees.

Conclusion: The two mirrors deviate the incident ray through an angle of 20 degrees.

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