Question

In a Young's double slit experiment, if the wavelength of light is increased by 50% and the distance between the slits is doubled, then the percentage change in fringe width is:

• A. 75
• B. 50
• C. 25
• D. 15

Hint:

When dealing with Young's double slit experiment, remember that fringe width depends directly on the wavelength and inversely on the slit separation. Any change in these factors will alter the fringe width accordingly.

Answer 1

The Correct Option is C

The fringe width \( \beta \) in Young's double slit experiment is given by: \[ \beta = \frac{\lambda D}{d} \] where: - \( \lambda \) is the wavelength of light, - \( D \) is the distance between the screen and the slits, and - \( d \) is the distance between the slits. If the wavelength \( \lambda \) is increased by 50%, then the new wavelength becomes \( 1.5\lambda \). Similarly, if the distance between the slits \( d \) is doubled, the new value of \( d \) becomes \( 2d \). Thus, the new fringe width \( \beta' \) will be: \[ \beta' = \frac{1.5\lambda D}{2d} = \frac{1}{2} \times 1.5 \times \frac{\lambda D}{d} = 1.5 \times \frac{\lambda D}{d} \] This shows that the new fringe width is 1.5 times the original fringe width. Therefore, the percentage change in fringe width is: \[ \text{Percentage change} = \left( \frac{1.5 - 1}{1} \right) \times 100 = 50% \] Thus, the correct answer is option (3), 25%.

Answer 2

Step 1: Recall the formula for fringe width
The fringe width \( \beta \) in Young's double slit experiment is given by:
\[ \beta = \frac{\lambda D}{d} \]
where \( \lambda \) is the wavelength of light, \( D \) is the distance between the slits and the screen, and \( d \) is the distance between the two slits.

Step 2: Given changes
- Wavelength \( \lambda \) is increased by 50%, so new wavelength:
\[ \lambda' = 1.5 \lambda \]
- Distance between the slits \( d \) is doubled:
\[ d' = 2d \]
- Assume \( D \) remains constant.

Step 3: Calculate new fringe width
\[ \beta' = \frac{\lambda' D}{d'} = \frac{1.5 \lambda D}{2 d} = \frac{1.5}{2} \times \frac{\lambda D}{d} = 0.75 \beta \]

Step 4: Calculate percentage change in fringe width
Percentage change = \(\frac{\beta' - \beta}{\beta} \times 100 = (0.75 - 1) \times 100 = -25\% \)
This means fringe width decreases by 25%.

Step 5: Considering magnitude
The percentage change in fringe width is 25%.

Step 6: Conclusion
Therefore, the fringe width changes by 25% (decreases) due to the given changes.