In the context of Young’s double-slit experiment (YDSE) using white light, consider the following st

Question

In the context of Young’s double-slit experiment (YDSE) using white light, consider the following statements:
(A) A bright white fringe is formed at the center of the screen.
(B) Clear fringes of different colors are observed only in the first order.
(C) The first-order violet fringes are closer to the center of the screen than the first-order red fringes.
(D) The first-order red fringes are closer to the center of the screen than the first-order violet fringes.

Professor PC Thomas Classes · Answer

1. The Central White Fringe (Statement A)
At the exact center of the screen, the path difference ( $\Delta x$ ) for all wavelengths is zero. Since there is no phase shift, all colors (wavelengths) of the white light undergo constructive interference simultaneously. When all visible colors combine at one point, they appear as white light.

2. The Separation of Colors (Statement C)
The position of the $n^{	ext {th }}$ order bright fringe $\left(y_night)$ is determined by the formula:
$$
y_n=\frac{n \lambda D}{d}
$$
- Violet light has a shorter wavelength ( $\lambda \approx 400 \mathrm{~nm}$ ).
- Red light has a longer wavelength ( $\lambda \approx 700 \mathrm{~nm}$ ).
Because $y$ is directly proportional to $\lambda$, the violet fringe will always be physically closer to the center than the red fringe for the same order.

3. Fringes in Higher Orders (Statement B)
As the order $(n)$ increases, the fringe width for different colors causes them to overlap. For example, the red fringe of the 2nd order might overlap with the violet fringe of the 3rd order. This overlapping "blurs" the colors back into white or gray, which is why distinct, clear colors are typically only visible in the first order (lowest value of $n$ ).