Question

In a biprism experiment, using a light of wavelength \(4800\text{ Å}\), a steady interference pattern was obtained on a screen \(1\text{ m}\) away from the source. Now the source is replaced by another of wavelength \(6400\text{ Å}\) and the screen is moved away from it by \(20\text{ cm}\). The fringewidth will

• A. decrease by 40%.
• B. decrease by 60%.
• C. increase by 60%.
• D. increase by 40%.

Hint:

Fringe width is proportional to wavelength times screen distance. Find the ratio of the new to the old fringe width.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
In a biprism experiment the fringe width is \(\beta = \dfrac{\lambda D}{d}\), and \(d\) stays the same.

Step 2: Given Data
\(\lambda_1 = 4800\text{ Å}\), \(D_1 = 1\text{ m}\)
\(\lambda_2 = 6400\text{ Å}\), \(D_2 = 1 + 0.2 = 1.2\text{ m}\)

Step 3: Ratio
\(\dfrac{\beta_2}{\beta_1} = \dfrac{6400 \times 1.2}{4800 \times 1} = 1.6\)

Step 4: Percentage Change
The change is \((1.6 - 1) \times 100 = 60\%\), an increase.

Final Answer:
The fringe width increases by 60%. \[ \boxed{\text{(C) }\text{increase by 60\%}} \]