Velocity of light in glass whose refractive index with respect to air is 1.5 is `2 xx10^(8) m//s` and in certain liquid the velocity of light found to be `2.5 xx10^(8)` m/s . The refractive index of the liquid with respect to air is

Options

A. 0.64
B. 0.8
C. 1.2
D. 1.44

Answer

To find the refractive index of the liquid with respect to air, we can use the relationship between the speed of light in a medium and its refractive index. The refractive index (μ) is given by the formula:

\[ \mu = \frac{c}{v} \]

where:
- \( c \) is the speed of light in vacuum (approximately \( 3 \times 10^8 \, m/s \)),
- \( v \) is the speed of light in the medium.

### Step-by-step Solution:

1. **Identify the given values:**
- Refractive index of glass with respect to air (\( \mu_g \)) = 1.5
- Speed of light in glass (\( v_g \)) = \( 2 \times 10^8 \, m/s \)
- Speed of light in liquid (\( v_l \)) = \( 2.5 \times 10^8 \, m/s \)

2. **Calculate the refractive index of glass:**
Using the formula for refractive index:
\[ \mu_g = \frac{c}{v_g} \]
Rearranging gives:
\[ c = \mu_g \cdot v_g \]
Substituting the values:
\[ c = 1.5 \cdot (2 \times 10^8) = 3 \times 10^8 \, m/s \]

3. **Calculate the refractive index of the liquid:**
Using the same formula for the liquid:
\[ \mu_l = \frac{c}{v_l} \]
Substituting \( c \) and \( v_l \):
\[ \mu_l = \frac{3 \times 10^8}{2.5 \times 10^8} \]

4. **Simplify the expression:**
\[ \mu_l = \frac{3}{2.5} = \frac{30}{25} = \frac{6}{5} = 1.2 \]

5. **Conclusion:**
The refractive index of the liquid with respect to air is \( \mu_l = 1.2 \).

### Final Answer:
The refractive index of the liquid with respect to air is **1.2**.