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

To solve the problem and determine the truth of the given statements, we need to understand the phenomenon of Young's double slit experiment.

• Angular Separation in Young’s Double Slit Experiment:

  In a Young's double slit experiment, the angular separation \theta of the fringes is given by the formula:

  \theta = \frac{\lambda}{d}

  where \lambda is the wavelength of the light used, and d is the distance between the slits.

• Analysis of Statement I:

  Statement I claims that the angular separation of fringes will increase as the screen is moved away from the plane of the slits. This is incorrect because angular separation \theta is independent of the screen distance. It depends only on \lambda and d. Thus, moving the screen does not affect the angular separation.

• Analysis of Statement II:

  Statement II says that the angular separation of fringes will increase when a monochromatic source is replaced by another monochromatic source of higher wavelength. According to the formula \theta = \frac{\lambda}{d}, increasing the wavelength \lambda will increase the angular separation \theta, as long as d remains constant. Therefore, Statement II is true.

Based on the above analysis:

• Correct Answer: Statement I is false but Statement II is true.