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 Question:
In an interference experiment (like Fresnel's biprism or Young's double slit), the wavelength of the light source is increased from $5000\text{\AA}$ to $6400\text{\AA}$. We must calculate the percentage change in the fringe width.

Step 2: Key Formula or Approach:
The fringe width ($X$ or $\beta$) is directly proportional to the wavelength of light ($\lambda$):
$$X = \frac{\lambda D}{d} \implies X \propto \lambda$$
Percentage change is calculated as:
$$%\text{ Change} = \frac{X_2 - X_1}{X_1} \times 100% = \frac{\lambda_2 - \lambda_1}{\lambda_1} \times 100%$$

Step 3: Detailed Explanation:
Given initial wavelength $\lambda_1 = 5000\text{\AA}$.
Given final wavelength $\lambda_2 = 6400\text{\AA}$.
Since $\lambda_2 > \lambda_1$, the fringe width will definitively increase. This immediately eliminates options (a) and (b).
Now, calculate the exact percentage increase:
$$\text{Increase} = \frac{6400 - 5000}{5000} \times 100%$$
$$\text{Increase} = \frac{1400}{5000} \times 100%$$
Cancel the zeroes:
$$\text{Increase} = \frac{14}{50} \times 100% = 14 \times 2% = 28%$$

Step 4: Final Answer:
The fringe width will increase by 28%, matching option (d).