Question

In a biprism experiment, source of light of wavelength 5000\AA{ is replaced by a source of 6400\AA{}. The fringe width will ______.

• A. decrease by 48%
• B. decrease by 28%
• C. increase by 48%
• D. increase by 28%

Hint:

Because fringe width is strictly linear with wavelength, replacing blue light ($\sim 4000\text{\AA}$) with red light ($\sim 8000\text{\AA}$) will always exactly double the thickness of your interference fringes on the screen.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Fringe width ($W$) is directly proportional to the wavelength ($\lambda$) of light used: $W = \frac{\lambda D}{d}$.

Step 2: Formula Application:
Percentage change $= \frac{\lambda_2 - \lambda_1}{\lambda_1} \times 100$.

Step 3: Explanation:
$\lambda_1 = 5000$\AA, $\lambda_2 = 6400$\AA. Change $= \frac{6400 - 5000}{5000} \times 100 = \frac{1400}{5000} \times 100 = 28%$. Since the wavelength increased, the fringe width also increases.

Step 4: Final Answer:
The fringe width will increase by 28%.