Question

For Young's double slit experiment, two statements are given below: 

Statement I: If screen is moved away from the plane of slits, angular separation of the fringes remians constant. 

Statement II: If the monochromatic source is replaced by another monochromatic source of larger wavelength, the angular separation of fringes decreases. In the light of the above statements, choose the correct answer from the options given below:

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

Answer 1

The Correct Option is D

To solve this problem, let's analyze both statements based on the principles of Young's double-slit experiment:

Statement I: When the screen is moved away from the plane of slits, the angular separation of the fringes remains constant.

In Young's double-slit experiment, the angular separation \( \theta \) of the fringes is determined by the formula: \[\theta = \dfrac{\lambda}{d}\] where \( \lambda \) is the wavelength of the light used and \( d \) is the separation between the slits. Since neither the wavelength \( \lambda \) nor the slit separation \( d \) changes when the screen is moved, the angular separation \( \theta \) remains unchanged. Thus, Statement I is true.

Statement II: If the monochromatic source is replaced by another monochromatic source of larger wavelength, the angular separation of fringes decreases.

Using the same formula for angular separation, \[\theta = \dfrac{\lambda}{d}\], we can see that if the wavelength \( \lambda \) increases, the angular separation \( \theta \) will increase since the separation \( d \) between the slits is constant. Therefore, the angular separation actually increases with a larger wavelength, making Statement II false.

Based on this analysis, the correct answer is: Statement I is true but Statement II is false.