A ray gets successively reflected from two mirrors inclined at an angle of `40^(@)`. If the angle of incidence on the first mirror is `60^(@)`, then the net deviation of this ray is -

Options

A. `40^(@)`
B. `280^(@)`
C. `80^(@)`
D. `100^(@)`

Explanation

To find the net deviation of a ray that gets successively reflected from two mirrors inclined at an angle of \(40^\circ\) with an angle of incidence on the first mirror of \(60^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Angle between the two mirrors, \(\theta = 40^\circ\)
- Angle of incidence on the first mirror, \(i_1 = 60^\circ\)

2. **Determine the Angle of Reflection:**
- According to the law of reflection, the angle of reflection is equal to the angle of incidence. Therefore, the angle of reflection from the first mirror, \(r_1\), is also \(60^\circ\).

3. **Calculate the Angle of Incidence on the Second Mirror:**
- The ray reflects off the first mirror and strikes the second mirror. The angle of incidence on the second mirror can be calculated using the relationship:
\[ i_2 = r_1 + \theta \]
- Substituting the values:
\[ i_2 = 60^\circ + 40^\circ = 100^\circ \]

4. **Determine the Angle of Reflection from the Second Mirror:**
- Again, applying the law of reflection, the angle of reflection from the second mirror, \(r_2\), will be equal to the angle of incidence on it:
\[ r_2 = i_2 = 100^\circ \]

5. **Calculate the Net Deviation:**
- The net deviation (\(\Delta\)) of the ray can be calculated using the formula:
\[ \Delta = 360^\circ - 2\theta \]
- Substituting the value of \(\theta\):
\[ \Delta = 360^\circ - 2 \times 40^\circ = 360^\circ - 80^\circ = 280^\circ \]

6. **Final Result:**
- Therefore, the net deviation of the ray is \(280^\circ\).