A ray of light is travelling from glass to air. The angle of incidence in glass is `35^(@)`, and angle of refraction in air `60^(@)`. What is the refractive index of glass w.r.t. air ?

Options

A. `1.9`
B. `0.5`
C. `1.51`
D. `2.0`

Explanation

To find the refractive index of glass with respect to air when a ray of light travels from glass to air, we can use Snell's Law, which states:

\[ n_1 \sin(i) = n_2 \sin(r) \]

Where:
- \( n_1 \) is the refractive index of the first medium (glass in this case),
- \( n_2 \) is the refractive index of the second medium (air),
- \( i \) is the angle of incidence,
- \( r \) is the angle of refraction.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Angle of incidence \( i = 35^\circ \)
- Angle of refraction \( r = 60^\circ \)
- \( \sin(35^\circ) = 0.5736 \)

2. **Use Snell's Law:**
Since we are looking for the refractive index of glass with respect to air, we can rearrange Snell's Law:

\[ n_{glass} = \frac{n_{air} \sin(r)}{\sin(i)} \]

We know that the refractive index of air \( n_{air} \) is approximately 1. Therefore, the equation simplifies to:

\[ n_{glass} = \frac{\sin(r)}{\sin(i)} \]

3. **Calculate \( \sin(60^\circ) \):**
We know that:

\[ \sin(60^\circ) = \frac{\sqrt{3}}{2} \approx 0.8660 \]

4. **Substitute the Values into the Equation:**
Now substitute the values into the equation:

\[ n_{glass} = \frac{\sin(60^\circ)}{\sin(35^\circ)} = \frac{0.8660}{0.5736} \]

5. **Perform the Calculation:**
Now calculate the value:

\[ n_{glass} \approx \frac{0.8660}{0.5736} \approx 1.51 \]

### Final Answer:
The refractive index of glass with respect to air is approximately **1.51**.

---