A monochromatic rar is incident on a glass slab with glancing angle `30^(@)` with the surface, If the refractive index of glass with respect to air is `sqrt(3)`, the angle of refraction in the glass slab is

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `70^(@)`

Answer

To solve the problem of finding the angle of refraction in the glass slab when a monochromatic ray is incident at a glancing angle of \(30^\circ\) with the surface, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information:**
- The incident angle with respect to the surface is \(30^\circ\).
- The refractive index of glass with respect to air is \(\sqrt{3}\).
- The refractive index of air (\(n_1\)) is \(1\).

2. **Determine the Angle of Incidence:**
- The angle of incidence (\(I\)) is measured with respect to the normal. Since the glancing angle is \(30^\circ\) with the surface, the angle with respect to the normal is:
\[ I = 90^\circ - 30^\circ = 60^\circ \]

3. **Apply Snell's Law:**
- Snell's Law states that:
\[ n_1 \sin I = n_2 \sin R \]
- Here, \(n_1 = 1\) (for air), \(n_2 = \sqrt{3}\) (for glass), \(I = 60^\circ\), and \(R\) is the angle of refraction we need to find.

4. **Substitute the Values into Snell's Law:**
- Substitute the known values into the equation:
\[ 1 \cdot \sin(60^\circ) = \sqrt{3} \cdot \sin R \]

5. **Calculate \(\sin(60^\circ)\):**
- We know that:
\[ \sin(60^\circ) = \frac{\sqrt{3}}{2} \]
- Therefore, the equation becomes:
\[ \frac{\sqrt{3}}{2} = \sqrt{3} \cdot \sin R \]

6. **Solve for \(\sin R\):**
- Divide both sides by \(\sqrt{3}\):
\[ \frac{\sqrt{3}}{2\sqrt{3}} = \sin R \]
- This simplifies to:
\[ \sin R = \frac{1}{2} \]

7. **Determine the Angle of Refraction \(R\):**
- The angle \(R\) for which \(\sin R = \frac{1}{2}\) is:
\[ R = 30^\circ \]

### Final Answer:
The angle of refraction in the glass slab is \(30^\circ\).