In Young's experiment, the wavelength of red light is `7.8xx10^(-5)` cm and that of blue light is `5.2 xx 10^(-5)` cm. The value of n for which (n + 1)th blue light band coincides with nth red band is

Options

A. 4
B. 2
C. 3
D. 1

Explanation

To solve the problem, we need to find the value of \( n \) for which the \( (n + 1) \)th blue light band coincides with the \( n \)th red band in Young's double-slit experiment.

### Step-by-Step Solution:

1. **Identify the Wavelengths**:
- Wavelength of red light, \( \lambda_r = 7.8 \times 10^{-5} \) cm.
- Wavelength of blue light, \( \lambda_b = 5.2 \times 10^{-5} \) cm.

2. **Understand the Condition for Coincidence**:
- The condition for the \( (n + 1) \)th blue light band to coincide with the \( n \)th red light band can be expressed as:
\[ n \lambda_r = (n + 1) \lambda_b \]

3. **Substitute the Wavelengths**:
- Substitute the values of \( \lambda_r \) and \( \lambda_b \) into the equation:
\[ n (7.8 \times 10^{-5}) = (n + 1)(5.2 \times 10^{-5}) \]

4. **Expand the Equation**:
- Expanding the right-hand side gives:
\[ n (7.8 \times 10^{-5}) = n (5.2 \times 10^{-5}) + (5.2 \times 10^{-5}) \]

5. **Rearranging the Equation**:
- Rearranging the equation leads to:
\[ n (7.8 \times 10^{-5}) - n (5.2 \times 10^{-5}) = 5.2 \times 10^{-5} \]
- Factor out \( n \):
\[ n \left(7.8 \times 10^{-5} - 5.2 \times 10^{-5}\right) = 5.2 \times 10^{-5} \]

6. **Calculate the Coefficient**:
- Calculate \( 7.8 - 5.2 = 2.6 \):
\[ n (2.6 \times 10^{-5}) = 5.2 \times 10^{-5} \]

7. **Solve for \( n \)**:
- Dividing both sides by \( 2.6 \times 10^{-5} \):
\[ n = \frac{5.2 \times 10^{-5}}{2.6 \times 10^{-5}} = 2 \]

### Final Answer:
The value of \( n \) for which the \( (n + 1) \)th blue light band coincides with the \( n \)th red band is \( n = 2 \).

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