The difference of speed of light in the two media A and `B (v_a-v_b)` is `2.6 xx 10^7` m/s. If the refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium A is: (Given: speed of light in vacuum `c=3 xx 10^6 ms^( -1)`)

Options

A. 1.303
B. 1.318
C. 1.13
D. 0.12

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the relationship between speed of light and refractive index
The speed of light in a medium is given by the formula:
\[ v = \frac{c}{\mu} \]
where \( v \) is the speed of light in the medium, \( c \) is the speed of light in vacuum, and \( \mu \) is the refractive index of the medium.

### Step 2: Calculate the speed of light in medium B
Given that the refractive index of medium B (\( \mu_B \)) is 1.47, we can calculate the speed of light in medium B (\( v_B \)):
\[ v_B = \frac{c}{\mu_B} = \frac{3 \times 10^8 \, \text{m/s}}{1.47} \]

Calculating this gives:
\[ v_B \approx 2.04 \times 10^8 \, \text{m/s} \]

### Step 3: Use the difference in speed to find the speed of light in medium A
We know that the difference in speed between medium A and medium B is given as:
\[ v_A - v_B = 2.6 \times 10^7 \, \text{m/s} \]

From this, we can express \( v_A \):
\[ v_A = v_B + 2.6 \times 10^7 \]

Substituting the value of \( v_B \):
\[ v_A = 2.04 \times 10^8 + 2.6 \times 10^7 \]
\[ v_A = 2.04 \times 10^8 + 0.26 \times 10^8 \]
\[ v_A = 2.3 \times 10^8 \, \text{m/s} \]

### Step 4: Calculate the refractive index of medium A
Now, we can find the refractive index of medium A (\( \mu_A \)):
\[ \mu_A = \frac{c}{v_A} = \frac{3 \times 10^8}{2.3 \times 10^8} \]

Calculating this gives:
\[ \mu_A \approx 1.304 \]

### Step 5: Find the ratio of the refractive indices
Finally, we need to find the ratio of the refractive index of medium B to medium A:
\[ \frac{\mu_B}{\mu_A} = \frac{1.47}{1.304} \]

Calculating this gives:
\[ \frac{\mu_B}{\mu_A} \approx 1.13 \]

### Final Answer
The ratio of the refractive index of medium B to medium A is approximately:
\[ \frac{\mu_B}{\mu_A} \approx 1.13 \]

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