In a plain mirror the angle between the incident ray and reflected ray is `60^@` . The angle between incident ray and mirror is?

Options

A. `60^@`
B. `30^@`
C. `90^@ `
D. `120^@`

Explanation

To solve the problem, we need to understand the relationship between the incident ray, the reflected ray, and the mirror surface. Here’s a step-by-step solution:

### Step 1: Understand the Angles
In optics, when light strikes a mirror, the angle of incidence (the angle between the incident ray and the normal to the mirror) is equal to the angle of reflection (the angle between the reflected ray and the normal). The normal is an imaginary line perpendicular to the surface of the mirror.

### Step 2: Define the Given Angles
We are given that the angle between the incident ray and the reflected ray is 60 degrees. Let's denote:
- \( \theta_i \) = angle of incidence
- \( \theta_r \) = angle of reflection

According to the law of reflection:
\[ \theta_i = \theta_r \]

### Step 3: Relate the Angles
The angle between the incident ray and the reflected ray can be expressed in terms of the angle of incidence and the angle of reflection:
\[ \text{Angle between incident ray and reflected ray} = \theta_i + \theta_r \]

Since \( \theta_i = \theta_r \), we can write:
\[ \text{Angle between incident ray and reflected ray} = \theta_i + \theta_i = 2\theta_i \]

### Step 4: Set Up the Equation
From the problem, we know that:
\[ 2\theta_i = 60^\circ \]

### Step 5: Solve for the Angle of Incidence
To find \( \theta_i \):
\[ \theta_i = \frac{60^\circ}{2} = 30^\circ \]

### Step 6: Conclusion
The angle between the incident ray and the mirror (which is the angle of incidence) is \( 30^\circ \).

### Final Answer
The angle between the incident ray and the mirror is \( 30^\circ \).

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