The velocity of light in a glass of refractive index 1.5 is `2 x ×10^(8) m s^(-1).` Its velocity in a certain liquid is found to be `2.5 x× 10^(8) m s^(-1).` The refractive index of the liquid with respect to air is

Options

A. `1.44`
B. `1.64`
C. `1.2`
D. `0.8`

Answer

To find the refractive index of the liquid with respect to air, we can follow these steps:

### Step 1: Understand the formula for refractive index
The refractive index (n) of a medium with respect to air (or vacuum) is given by the formula:
\[ n = \frac{c}{v} \]
where:
- \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \, \text{m/s} \)),
- \( v \) is the speed of light in the medium.

### Step 2: Identify the given values
From the problem, we have:
- The speed of light in the liquid, \( v_{\text{liquid}} = 2.5 \times 10^8 \, \text{m/s} \).
- The speed of light in vacuum, \( c = 3 \times 10^8 \, \text{m/s} \).

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the refractive index formula for the liquid:
\[ n_{\text{liquid}} = \frac{c}{v_{\text{liquid}}} \]
\[ n_{\text{liquid}} = \frac{3 \times 10^8 \, \text{m/s}}{2.5 \times 10^8 \, \text{m/s}} \]

### Step 4: Calculate the refractive index
Now, perform the division:
\[ n_{\text{liquid}} = \frac{3}{2.5} = 1.2 \]

### Step 5: Conclusion
Thus, the refractive index of the liquid with respect to air is:
\[ n_{\text{liquid}} = 1.2 \]

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

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