Let’s analyze and solve each problem from the image step by step.

Problem 1:

Question: A ray of light is incident towards a plane mirror at an angle of $30^\circ$ with the mirror surface. What will be the angle of reflection?

Solution:

The law of reflection states: $\text{Angle of incidence} = \text{Angle of reflection}$ However, the angle of incidence ($i$) is measured relative to the normal (perpendicular line to the mirror surface), not the mirror surface itself.

Given:

• The angle between the ray and the mirror surface = $30^\circ$

To find the angle of incidence: $i = 90^\circ - 30^\circ = 60^\circ$

By the law of reflection: $\text{Angle of reflection} = 60^\circ$

Answer: The angle of reflection is $60^\circ$.

Problem 2:

Question: A ray of light strikes a completely mirrored surface where the mirrors meet at a right angle. Given one angle as $60^\circ$, determine the unknown angle $\theta$.

Solution:

The mirrors form a $90^\circ$ corner. The incident ray first reflects off the first mirror and then reflects off the second mirror.

From the geometry of the situation:

1. The first angle of incidence is $60^\circ$ (given).
2. The reflected ray forms complementary angles with the mirrors and follows the law of reflection.

In the triangle formed by the path of the light and the mirrors:

• The sum of internal angles in a triangle is $180^\circ$.
• Two known angles are:
  • $60^\circ$ (given angle),
  • $90^\circ$ (from the right angle between mirrors).

Thus, the unknown angle $\theta$ is: $\theta = 180^\circ - 90^\circ - 60^\circ = 30^\circ$

Answer: The unknown angle $\theta$ is $30^\circ$.

Problem 3:

This problem is cut off, and I cannot see all the details in the diagram or the full description.

If you’d like, you can share the remaining part of the problem for me to solve it thoroughly.

Do you want me to clarify or expand on any part of these solutions?

Related Questions:

1. What is the law of reflection, and how is it applied?
2. How do you calculate angles of incidence and reflection from a surface?
3. How do mirrors placed at different angles affect the reflected ray’s path?
4. What happens if two mirrors meet at an angle other than $90^\circ$?
5. How do you determine the path of light in a set of multiple mirrors?

Tip: Always measure the angle of incidence and reflection relative to the normal to the surface, not the surface itself.