A ray of light makes an angle of `10^@` with the horizontal and strikes a plane mirror which is inclined at an angle `theta` to the horizontal. The angle `theta` for which the reflected ray becomes vertical, is

Options

A. `40^`
B. `50^@`
C. `80^@`
D. `100^@`

Explanation

To solve the problem, we need to analyze the situation step by step using the laws of reflection.

### Step 1: Understand the angles involved
- The ray of light makes an angle of \(10^\circ\) with the horizontal. This angle is the angle of incidence (\(i\)).
- The mirror is inclined at an angle \(\theta\) to the horizontal.

### Step 2: Determine the angle of incidence with respect to the mirror
- The angle of incidence (\(i\)) with respect to the normal to the mirror is given by:
\[ i = 90^\circ - (\theta + 10^\circ) \]
- This is because the angle of incidence is measured from the normal, which is perpendicular to the surface of the mirror.

### Step 3: Apply the law of reflection
- According to the law of reflection, the angle of reflection (\(r\)) is equal to the angle of incidence (\(i\)):
\[ r = i \]
- Therefore, we can write:
\[ r = 90^\circ - (\theta + 10^\circ) \]

### Step 4: Determine the condition for the reflected ray to be vertical
- For the reflected ray to be vertical, the angle of reflection must be \(90^\circ\):
\[ r = 90^\circ \]
- Substituting this into the equation from Step 3, we get:
\[ 90^\circ = 90^\circ - (\theta + 10^\circ) \]

### Step 5: Solve for \(\theta\)
- Rearranging the equation gives:
\[ \theta + 10^\circ = 0 \]
- Therefore, we find:
\[ \theta = -10^\circ \]

### Conclusion
The angle \(\theta\) for which the reflected ray becomes vertical is \(-10^\circ\).

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