Question

Given below are two statements :
Statement I : In a Young's double slit experiment, the angular separation of fringes will increase as the screen is moved away from the plane of the slits
Statement II : In a Young's double slit experiment, the angular separation of fringes will increase when monochromatic source is replaced by another monochromatic source of higher wavelength
In the light of the above statements, choose the correct answer from the options given below :

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true but Statement II is false
• D. Statement I is false but Statement II is true

Hint:

Angular width ($\lambda/d$) is an intrinsic property of the slit arrangement, while linear width ($\lambda D/d$) depends on the screen's position.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Angular separation \( \theta \) in YDSE is the angle subtended by a fringe width at the center of the slits. It differs from linear fringe width \( \beta \).

Step 2: Key Formula or Approach:
1. Linear fringe width: \( \beta = \frac{\lambda D}{d} \)
2. Angular separation: \( \theta = \frac{\beta}{D} = \frac{\lambda}{d} \)

Step 3: Detailed Explanation:
- Evaluation of Statement I: The formula for angular separation is \( \theta = \frac{\lambda}{d} \). This expression does not involve the distance to the screen ($D$). Therefore, moving the screen away does not change the angular separation. Statement I is false.
- Evaluation of Statement II: From \( \theta = \frac{\lambda}{d} \), it is clear that \( \theta \propto \lambda \). If the source is replaced by one with a higher wavelength, the angular separation will increase. Statement II is true.

Step 4: Final Answer:
Statement I is false and Statement II is true.