If the refractive indices of a prism for red, yellow and violet colours be `1.61, 1.63` and `1.65` respectively, then the dispersive power of the prism will be

Options

A. `(1.65-1.62)/(1.61-1)`
B. `(1.62-1.61)/(1.65-1)`
C. `(1.65-1.61)/(1.63-1)`
D. `(1.65-1.63)/(1.61-1)`

Explanation

To calculate the dispersive power of the prism, we can use the formula:

\[ P = \frac{\mu_v - \mu_r}{\mu_y - 1} \]

where:
- \( P \) is the dispersive power,
- \( \mu_v \) is the refractive index for violet light,
- \( \mu_r \) is the refractive index for red light,
- \( \mu_y \) is the refractive index for yellow light.

### Step 1: Identify the refractive indices
From the question, we have the following values:
- \( \mu_r = 1.61 \) (for red)
- \( \mu_y = 1.63 \) (for yellow)
- \( \mu_v = 1.65 \) (for violet)

### Step 2: Substitute the values into the formula
Now, we will substitute these values into the dispersive power formula:

\[ P = \frac{1.65 - 1.61}{1.63 - 1} \]

### Step 3: Calculate the numerator
Calculate the difference in the numerator:

\[ 1.65 - 1.61 = 0.04 \]

### Step 4: Calculate the denominator
Calculate the difference in the denominator:

\[ 1.63 - 1 = 0.63 \]

### Step 5: Calculate the dispersive power
Now, substitute the results back into the formula:

\[ P = \frac{0.04}{0.63} \]

### Step 6: Perform the division
Now, perform the division:

\[ P \approx 0.0635 \]

### Final Answer
Thus, the dispersive power of the prism is approximately \( 0.0635 \).

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