Question

In a Young's double slit experiment which of the following statements is NOT true?

• A. Angular separation of the fringes remains constant when the screen is moved away from the plane of the slits.
• B. Fringe separation increases when the separation between the two slits decreases.
• C. Sharpness of the fringe pattern decreases when the source slit width increases.
• D. Distance between the fringes decreases when the separation between slits and the Screen increases.
• E. The central fringe is white when the monochromatic source is replaced by a white light source.

Answer 1

The Correct Option is D

Given:

• Young’s double slit experiment setup.
• Five statements (A-E) about fringe properties.

Step 1: Analyze Each Statement

(A) Angular separation remains constant when screen is moved away.

True. The angular separation (\( \theta \approx \lambda/d \)) depends only on wavelength (\( \lambda \)) and slit separation (\( d \)), not on screen distance (\( D \)).

(B) Fringe separation increases when slit separation decreases.

True. Fringe separation (\( \Delta y = \lambda D/d \)) is inversely proportional to slit separation (\( d \)).

(C) Sharpness decreases when source slit width increases.

True. Increasing source slit width reduces coherence, causing fringes to blur.

(D) Distance between fringes decreases when \( D \) (slit-screen distance) increases.

False. Fringe separation (\( \Delta y \)) is directly proportional to \( D \), so increasing \( D \) increases fringe distance.

(E) Central fringe is white with white light source.

True. All wavelengths constructively interfere at the center, producing a white fringe.

Conclusion:

The statement that is NOT true is (D), as it incorrectly claims fringe distance decreases with increasing \( D \).

Answer: \(\boxed{D}\)

Answer 2

Let's analyze each statement about Young's double-slit experiment:

(A) Angular separation of the fringes remains constant when the screen is moved away from the plane of the slits.

The angular separation is given by:

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

where:

• θ is the angular separation
• λ is the wavelength of light
• d is the separation between the slits

As λ and d are constant, the angular separation θ remains constant even if the screen is moved. This statement is TRUE.

(B) Fringe separation increases when the separation between the two slits decreases.

The fringe separation (β) is given by:

\[\beta = \frac{\lambda D}{d}\]

where:

• β is the fringe separation
• λ is the wavelength of light
• D is the distance between the slits and the screen
• d is the separation between the slits

If d decreases, β increases. This statement is TRUE.

(C) Sharpness of the fringe pattern decreases when the source slit width increases.

A wider source slit leads to less coherent light, which reduces the sharpness of the fringe pattern. This statement is TRUE.

(D) Distance between the fringes decreases when the separation between slits and the screen increases.

As shown in the formula for fringe separation (β) above, if d increases and other factors remain constant, β actually increases, not decreases. This statement is FALSE.

(E) The central fringe is white when the monochromatic source is replaced by a white light source.

With a white light source, all wavelengths constructively interfere at the central fringe, resulting in a white central fringe. This statement is TRUE.

Final Answer: The statement that is NOT true is \(\boxed{D}\)