A beam of light is incident on glass slab making an angle of `60^(@)` with the surface. The angle of refraction and the velocity of light in glass of R.I. 1.5 are

Options

A. `19^(@)28, 3 xx 10^(8)m//s`
B. `29^(@)28', 2 xx 10^(8)m//s`
C. `19^(@)28', 2 xx 10^(8)m//s`
D. `29^(@)28, 3 xx 10^(8)m//s`

Explanation

To solve the problem, we need to find the angle of refraction and the velocity of light in the glass slab given the angle of incidence and the refractive index of the glass.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Angle of incidence with respect to the surface = \(60^\circ\)
- Refractive index of glass (\(n_2\)) = 1.5
- Refractive index of air (\(n_1\)) = 1 (approximately)

2. **Calculate the Angle of Incidence:**
- The angle of incidence (\(I\)) with respect to the normal is calculated as:
\[ I = 90^\circ - 60^\circ = 30^\circ \]

3. **Apply Snell's Law:**
- Snell's Law states:
\[ n_1 \sin I = n_2 \sin R \]
- Substitute the known values:
\[ 1 \cdot \sin(30^\circ) = 1.5 \cdot \sin R \]
- We know that \(\sin(30^\circ) = \frac{1}{2}\):
\[ 1 \cdot \frac{1}{2} = 1.5 \cdot \sin R \]
- This simplifies to:
\[ \frac{1}{2} = 1.5 \cdot \sin R \]

4. **Solve for \(\sin R\):**
- Rearranging gives:
\[ \sin R = \frac{1/2}{1.5} = \frac{1}{3} \]

5. **Calculate the Angle of Refraction:**
- To find \(R\), take the inverse sine:
\[ R = \sin^{-1}\left(\frac{1}{3}\right) \]
- Using a calculator, we find:
\[ R \approx 19^\circ 28' \]

6. **Calculate the Velocity of Light in Glass:**
- The formula for the velocity of light in a medium is:
\[ v = \frac{c}{n} \]
- Where \(c\) is the speed of light in vacuum (\(3 \times 10^8 \, \text{m/s}\)) and \(n\) is the refractive index.
- Substitute the values:
\[ v = \frac{3 \times 10^8}{1.5} = 2 \times 10^8 \, \text{m/s} \]

### Final Answers:
- Angle of refraction \(R \approx 19^\circ 28'\)
- Velocity of light in glass \(v = 2 \times 10^8 \, \text{m/s}\)

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