two mirrors are inclined at anangle 50degree a ray of light strikes one mirror making angle 2o degree with one the deviation= 22o hw

To solve the problem involving two mirrors inclined at an angle of 50 degrees and a ray of light striking one of the mirrors, we need to analyze the situation step by step. The key concepts here are the laws of reflection and how angles of incidence and reflection relate to each other.

Understanding the Setup

We have two mirrors positioned at an angle of 50 degrees to each other. When a ray of light strikes one of the mirrors, it does so at an angle of 20 degrees with respect to the normal (the line perpendicular to the surface of the mirror). According to the law of reflection, the angle of incidence is equal to the angle of reflection.

Calculating the First Reflection

Let’s denote the first mirror as Mirror 1. When the ray strikes Mirror 1 at an angle of 20 degrees, the angle of reflection will also be 20 degrees. This means that the ray will reflect off Mirror 1 at an angle of 20 degrees relative to the normal.

Determining the Angle with Respect to the Second Mirror

Next, we need to find out how this reflected ray interacts with the second mirror (Mirror 2). Since the two mirrors are inclined at 50 degrees, we can calculate the angle between the reflected ray and the normal of Mirror 2.

• The angle between the normal of Mirror 1 and the normal of Mirror 2 is 50 degrees.
• The angle of reflection from Mirror 1 is 20 degrees.
• Thus, the angle of the reflected ray with respect to the normal of Mirror 2 can be calculated as follows:

Angle with respect to Mirror 2's normal = 50 degrees - 20 degrees = 30 degrees.

Calculating the Second Reflection

Now, when the ray strikes Mirror 2, it does so at an angle of 30 degrees to the normal. Applying the law of reflection again, the angle of reflection will also be 30 degrees. This means the ray will reflect off Mirror 2 at an angle of 30 degrees relative to its normal.

Finding the Total Deviation

To find the total deviation of the ray from its original path, we need to consider the angles involved. The total deviation can be calculated by adding the angles of incidence and reflection for both mirrors.

• From Mirror 1: 20 degrees (incident) + 20 degrees (reflected) = 40 degrees.
• From Mirror 2: 30 degrees (incident) + 30 degrees (reflected) = 60 degrees.

However, since the mirrors are inclined at 50 degrees, we need to adjust for this inclination. The total deviation can be calculated as follows:

Total deviation = (Angle of incidence on Mirror 1 + Angle of reflection from Mirror 1) + (Angle of incidence on Mirror 2 + Angle of reflection from Mirror 2) - 180 degrees (for the inclination of the mirrors).

Plugging in the values:

Total deviation = (20 + 20) + (30 + 30) - 50 = 40 + 60 - 50 = 50 degrees.

Final Result

Thus, the total deviation of the ray of light after reflecting off both mirrors is 50 degrees. This analysis illustrates how the angles of incidence and reflection, along with the inclination of the mirrors, play a crucial role in determining the path of light.