Match the following .
`{:(" (A) A plane mirror ( )","(a) Number of images d = 3 "),("(B) Principle used in a periscope ( )"," (b) Reflection of light"),(" (C ) During reflection ( )"," (c ) Shows lateral inversion "),(" (D) If " theta = 90^(@)"between two plane mirrors then ( )" ," (d) Intensity changes "):}`

Explanation

To solve the matching question, we will analyze each option and match them accordingly.

### Step-by-Step Solution:

1. **Identify the properties of a plane mirror (A)**:
- A plane mirror shows lateral inversion, meaning it flips the image left to right.
- Therefore, we can match (A) A plane mirror with (c) Shows lateral inversion.

2. **Understand the principle used in a periscope (B)**:
- A periscope operates on the principle of reflection of light. It uses mirrors to reflect light from one point to another.
- Hence, we match (B) Principle used in a periscope with (b) Reflection of light.

3. **Determine the number of images formed between two plane mirrors (C)**:
- The formula for the number of images (n) formed by two plane mirrors at an angle (θ) is given by:
\[ n = \frac{360}{\theta} - 1 \]
- If θ = 90°, then:
\[ n = \frac{360}{90} - 1 = 4 - 1 = 3 \]
- Therefore, we match (C) During reflection with (a) Number of images d = 3.

4. **Analyze the condition when θ = 90° between two plane mirrors (D)**:
- When the angle θ is 90°, the intensity of the light changes due to the reflection.
- Thus, we match (D) If θ = 90° between two plane mirrors then with (d) Intensity changes.

### Final Matching:
- (A) A plane mirror → (c) Shows lateral inversion
- (B) Principle used in a periscope → (b) Reflection of light
- (C) During reflection → (a) Number of images d = 3
- (D) If θ = 90° between two plane mirrors then → (d) Intensity changes