In Young's double-slit experiment, the y-coordinate of central maxima and 10th maxima are 2 cm and 5 cm, respectively, When the YDSE apparatus is immersed in a liquid of refreactive index 1.5, the corresponding y-coordinates will be

Options

A. 2 cm, 7.5 cm
B. 3 cm, 6 cm
C. 2 cm, 4 cm
D. `4//3 cm`, 103 cm

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the given information
In Young's double-slit experiment (YDSE), we know the y-coordinates of the central maxima and the 10th maxima:
- \( y_0 = 2 \, \text{cm} \) (central maxima)
- \( y_{10} = 5 \, \text{cm} \) (10th maxima)

### Step 2: Determine the fringe width (β)
The fringe width (β) is given by the formula:
\[ y_n = y_0 + n \cdot \beta \]
For the 10th maxima (\( n = 10 \)):
\[ y_{10} = y_0 + 10 \cdot \beta \]
Substituting the known values:
\[ 5 = 2 + 10 \cdot \beta \]
Now, we can solve for β:
\[ 5 - 2 = 10 \cdot \beta \implies 3 = 10 \cdot \beta \implies \beta = \frac{3}{10} \, \text{cm} \]

### Step 3: Effect of immersion in a liquid
When the apparatus is immersed in a liquid with a refractive index \( \mu = 1.5 \), the new fringe width \( \beta' \) is given by:
\[ \beta' = \frac{\beta}{\mu} \]
Substituting the value of β:
\[ \beta' = \frac{3/10}{1.5} = \frac{3}{10} \cdot \frac{1}{1.5} = \frac{3}{15} = \frac{1}{5} \, \text{cm} \]

### Step 4: Calculate the new y-coordinates
Now we can find the new y-coordinates after immersion in the liquid.

1. **For the central maxima (\( n = 0 \))**:
\[ y_0' = y_0 = 2 \, \text{cm} \]

2. **For the 10th maxima (\( n = 10 \))**:
\[ y_{10}' = y_0 + 10 \cdot \beta' = 2 + 10 \cdot \frac{1}{5} \]
Calculating this:
\[ y_{10}' = 2 + 2 = 4 \, \text{cm} \]

### Final Results
Thus, the new y-coordinates after immersion in the liquid are:
- Central maxima: \( y_0' = 2 \, \text{cm} \)
- 10th maxima: \( y_{10}' = 4 \, \text{cm} \)

### Summary
- The y-coordinate of the central maxima remains \( 2 \, \text{cm} \).
- The y-coordinate of the 10th maxima changes to \( 4 \, \text{cm} \).