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

Let's analyze each statement given in the context of Young's double slit experiment:

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

Explanation: The angular separation \(\theta\) of the fringes in the Young's double slit experiment is given by the formula:

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

where \(\lambda\) is the wavelength of light used and \(d\) is the distance between the slits. This formula indicates that the angular separation depends only on the wavelength of the light and the distance between the slits, and is independent of the distance from the slits to the screen. Hence, as the screen is moved away, the angular separation remains unchanged.

Conclusion: 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.

Explanation: From the same formula \(\theta = \frac{\lambda}{d}\), we can see that the angular separation of the fringes is directly proportional to the wavelength \(\lambda\). This means that if the wavelength increases, the angular separation will also increase, contrary to what is stated in Statement II.

Conclusion: Statement II is false.

Based on the analysis above, the correct answer is:

Statement I is true but Statement II is false.