Which of the following statements are correct?

Options

A. A ray of light is incident on a plane mirror and gets reflected. If the mirror is rotated through an angle `theta`, then the reflected ray gets deviated through angle `2theta`
B. A ray of light gets reflected successively from two mirrors which are mutually inclined. Angular deviation suffered by the ray does not depend upon an angle of incidence on first mirror
C. A plane mirror cannot form real image of a real object
D. If an object approached toward a plane mirror with velocity v, then the image approaches the object with velocity 2v.

Explanation

To determine which statements are correct regarding the behavior of light with mirrors, let's analyze each statement step by step.

### Step 1: Analyzing the First Statement
**Statement:** A ray of light is incident on a plane mirror and gets reflected. If a mirror is rotated about an angle of θ, then the reflected ray gets diverted through the angle of 2θ.

**Solution:**
1. Draw a diagram with a plane mirror and a ray of light incident on it.
2. Mark the incident angle (I) and the reflected angle (R). According to the law of reflection, I = R.
3. When the mirror is rotated by an angle θ, the normal to the mirror also rotates by θ.
4. The new angles of incidence and reflection will be I + θ and R + θ respectively.
5. The total deviation (Δ) of the reflected ray from its original path is given by Δ = 180° - (I + θ + R + θ).
6. Simplifying this gives Δ = 180° - 2I - 2θ, which shows that the deviation is indeed 2θ when the mirror is rotated by θ.

**Conclusion:** The first statement is correct.

### Step 2: Analyzing the Second Statement
**Statement:** A ray of light gets reflected successively from two mirrors which are mutually inclined. The angle of deviation suffered by the ray does not depend upon the angle of incidence on the first mirror.

**Solution:**
1. Draw two mirrors inclined at an angle θ.
2. Let the incident ray strike the first mirror at an angle α.
3. The angle of deviation after the first reflection can be calculated.
4. The second reflection will depend on the angle of inclination θ and the angle of incidence α.
5. The total deviation can be expressed as Δ = Δ1 + Δ2, where Δ1 and Δ2 are the deviations from each mirror.
6. After calculating, you will find that the total deviation is independent of the angle of incidence α.

**Conclusion:** The second statement is correct.

### Step 3: Analyzing the Third Statement
**Statement:** A plane mirror cannot form a real image of a real object.

**Solution:**
1. Consider a plane mirror and an object placed in front of it.
2. The image formed by a plane mirror is virtual, as it appears to be behind the mirror at the same distance as the object in front.
3. A real image is formed when light rays converge, which does not happen with a plane mirror.

**Conclusion:** The third statement is incorrect.

### Step 4: Analyzing the Fourth Statement
**Statement:** If an object approaches a plane mirror with the velocity v, then the image approaches with the velocity 2v.

**Solution:**
1. When an object moves towards the mirror with velocity v, the image also moves towards the mirror with the same velocity v.
2. The relative velocity of the image towards the object is the sum of their velocities, which is v (object) + v (image) = 2v.

**Conclusion:** The fourth statement is correct.

### Final Conclusion
The correct statements are:
1. The first statement is correct.
2. The second statement is correct.
3. The third statement is incorrect.
4. The fourth statement is correct.

### Summary of Correct Statements
- Correct: 1, 2, and 4.
- Incorrect: 3.