In Young's double slit experimental setup, if the wavelength alone is doubled, the band width `beta` becomes

Options

A. `(beta)/(2)`
B. `2beta`
C. `4beta`
D. `beta`

Explanation

To solve the problem, we need to understand the relationship between the wavelength of light and the bandwidth (fringe width) in Young's double slit experiment.

### Step-by-Step Solution:

1. **Understand the Concept of Bandwidth (Fringe Width)**:
- In Young's double slit experiment, the bandwidth (β) is defined as the distance between two consecutive bright or dark fringes on the screen.

2. **Formula for Bandwidth**:
- The formula for bandwidth (β) is given by:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) = wavelength of light
- \( D \) = distance from the slits to the screen
- \( d \) = distance between the two slits

3. **Effect of Doubling the Wavelength**:
- If the wavelength \( \lambda \) is doubled, we can express the new wavelength as:
\[ \lambda' = 2\lambda \]

4. **Substituting the New Wavelength into the Formula**:
- Now, substituting \( \lambda' \) into the bandwidth formula:
\[ \beta' = \frac{\lambda' D}{d} = \frac{(2\lambda) D}{d} = 2 \left(\frac{\lambda D}{d}\right) = 2\beta \]

5. **Conclusion**:
- Therefore, when the wavelength is doubled, the new bandwidth \( \beta' \) becomes:
\[ \beta' = 2\beta \]

### Final Answer:
If the wavelength alone is doubled, the bandwidth \( \beta \) becomes \( 2\beta \).

---