Refractive index of glass with respect to medium is `(4)/(3)`. If `v_(m) - v_(g) = 6.25 xx 10^(7)` m/s., then velocity of light in medium is

Options

A. `2.5xx10^(8)` m/s
B. `0.125xx10^(8)` m/s
C. `1.5xx10^(7)` m/s
D. `3xx10^(7)` m/s

Explanation

To find the velocity of light in the medium (V_m), we can follow these steps:

### Step 1: Understand the relationship between refractive index and velocity
The refractive index (μ) of glass with respect to the medium is given as \( \frac{4}{3} \). The refractive index can be expressed in terms of the velocities of light in air (c), the medium (V_m), and glass (V_g) as follows:
\[ \mu = \frac{c}{V} \]
For glass with respect to the medium, we can write:
\[ \mu_{glass, medium} = \frac{V_m}{V_g} = \frac{4}{3} \]

### Step 2: Rearranging the equation
From the equation above, we can rearrange it to express V_m in terms of V_g:
\[ V_m = \frac{4}{3} V_g \]

### Step 3: Use the given information
We are given that:
\[ V_m - V_g = 6.25 \times 10^7 \, \text{m/s} \]
Substituting \( V_m \) from Step 2 into this equation gives:
\[ \frac{4}{3} V_g - V_g = 6.25 \times 10^7 \]

### Step 4: Simplifying the equation
To simplify, we can express \( V_g \) in a common fraction:
\[ \frac{4}{3} V_g - \frac{3}{3} V_g = 6.25 \times 10^7 \]
This simplifies to:
\[ \frac{1}{3} V_g = 6.25 \times 10^7 \]

### Step 5: Solve for V_g
Multiplying both sides by 3 to solve for \( V_g \):
\[ V_g = 3 \times 6.25 \times 10^7 = 18.75 \times 10^7 \, \text{m/s} \]

### Step 6: Calculate V_m
Now that we have \( V_g \), we can find \( V_m \):
\[ V_m = \frac{4}{3} V_g = \frac{4}{3} \times 18.75 \times 10^7 \]
Calculating this gives:
\[ V_m = 25 \times 10^7 \, \text{m/s} = 2.5 \times 10^8 \, \text{m/s} \]

### Final Answer
Thus, the velocity of light in the medium is:
\[ \boxed{2.5 \times 10^8 \, \text{m/s}} \]

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