Two plane mirrors at an angle such that a ray incident on a mirror undergoes a total deviation of `240^(@)` after two reflections:

Options

A. the angle between the mirrors is `60^(@)`
B. the number of images formed by this system will be `5` , if an object is placed symmetrically between the mirrors
C. the number of images will be 5 if an object is kept unsymmetrical between the mirrors
D. a ray will retrace its path after 2 successive reflections , if the angle of incidence on one mirror is `60^(@)`

Explanation

To solve the problem of finding the angle between two plane mirrors given that a ray incident on one mirror undergoes a total deviation of 240 degrees after two reflections, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Deviation**:
- When a ray of light reflects off a mirror, the angle of deviation (D) is defined as the angle between the incident ray and the final ray after reflection. For a single reflection, the deviation is given by the formula:
\[ D = 180^\circ - 2i \]
where \(i\) is the angle of incidence.

2. **Total Deviation After Two Reflections**:
- Since the ray reflects off two mirrors, we need to consider the total deviation after both reflections. If the angle between the mirrors is \(\theta\), the total deviation after two reflections can be expressed as:
\[ D_{total} = D_1 + D_2 = (180^\circ - 2i_1) + (180^\circ - 2i_2) \]
- This simplifies to:
\[ D_{total} = 360^\circ - 2(i_1 + i_2) \]

3. **Relate the Angles to the Angle Between Mirrors**:
- The angles of incidence \(i_1\) and \(i_2\) can be related to the angle \(\theta\) between the mirrors. The relationship is:
\[ i_2 = \theta - i_1 \]
- Substituting this into the total deviation equation gives:
\[ D_{total} = 360^\circ - 2(i_1 + (\theta - i_1)) = 360^\circ - 2\theta \]

4. **Set Up the Equation**:
- We know from the problem statement that the total deviation \(D_{total}\) is 240 degrees. Thus, we can set up the equation:
\[ 360^\circ - 2\theta = 240^\circ \]

5. **Solve for \(\theta\)**:
- Rearranging the equation gives:
\[ 2\theta = 360^\circ - 240^\circ \]
\[ 2\theta = 120^\circ \]
\[ \theta = 60^\circ \]

6. **Conclusion**:
- The angle between the two mirrors is \(60^\circ\).