In a Fresnel biprism experiment, the two positions of lens give separation between the slits as 16cm and 9cm respectively. What is the actual distance of separation?

Options

A. 12 cm
B. 12.5 cm
C. 13 cm
D. 14 cm

Explanation

To solve the problem of finding the actual distance of separation in a Fresnel biprism experiment, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- The first position of the lens gives a separation \( d_1 = 16 \, \text{cm} \).
- The second position of the lens gives a separation \( d_2 = 9 \, \text{cm} \).

2. **Use the Formula for Actual Distance of Separation**:
- The actual distance of separation \( d \) can be calculated using the formula:
\[ d = \sqrt{d_1 \times d_2} \]

3. **Substitute the Values into the Formula**:
- Substitute \( d_1 \) and \( d_2 \) into the formula:
\[ d = \sqrt{16 \times 9} \]

4. **Calculate the Product Inside the Square Root**:
- Calculate \( 16 \times 9 \):
\[ 16 \times 9 = 144 \]

5. **Take the Square Root**:
- Now calculate the square root of 144:
\[ d = \sqrt{144} = 12 \, \text{cm} \]

6. **Final Answer**:
- The actual distance of separation is \( d = 12 \, \text{cm} \).

### Summary:
The actual distance of separation in the Fresnel biprism experiment is \( 12 \, \text{cm} \).

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