YDSE with white light
Young's Double Slit Experiment (YDSE) with White Light
Young's Double Slit Experiment (YDSE) is a classic physics experiment that demonstrates the wave nature of light. It was first performed by Thomas Young in 1801 to prove the wave theory of light. When monochromatic light is used in YDSE, it produces a clear pattern of bright and dark fringes. However, when white light is used, the pattern becomes more complex due to the presence of multiple wavelengths.
Understanding White Light in YDSE
White light is composed of a spectrum of colors, each with a different wavelength. When white light passes through the double slits, each wavelength diffracts and interferes differently, leading to a superposition of various fringe patterns.
Central Bright Fringe
The central bright fringe in a YDSE with white light is white because all wavelengths constructively interfere at the center. This is because the path difference for all wavelengths is zero at the center, leading to constructive interference.
Colored Fringes
On either side of the central white fringe, the pattern consists of a series of colored fringes. These fringes are due to the constructive and destructive interference of different wavelengths of light. The innermost fringes are violet as they have the shortest wavelength, and the outermost fringes are red as they have the longest wavelength.
Fringe Width
The fringe width for a given color in the spectrum can be calculated using the formula:
$$ w = \frac{\lambda D}{d} $$
where:
- ( w ) is the fringe width
- ( \lambda ) is the wavelength of light
- ( D ) is the distance between the slits and the screen
- ( d ) is the distance between the two slits
Since white light contains all visible wavelengths, each color will have a different fringe width, with red having the widest and violet the narrowest.
Differences and Important Points
Here is a table summarizing the differences and important points of YDSE with white light:
| Aspect | Monochromatic Light | White Light |
|---|---|---|
| Fringe Color | Uniform (color of the light used) | Central fringe is white, followed by colored fringes |
| Fringe Width | Uniform for all fringes | Varies with color; red has the widest, violet the narrowest |
| Fringe Visibility | Clear and distinct | Less distinct due to overlapping of colors |
| Path Difference | Same for all fringes | Varies with wavelength, leading to different fringe positions |
| Coherence | Required for clear pattern | Less coherent due to multiple wavelengths |
Examples
Example 1: Central Fringe
When white light is used in YDSE, the central fringe is always white. This is because all wavelengths have a path difference of zero at the center, leading to constructive interference.
Example 2: Colored Fringes
If the distance between the slits and the screen (D) is 1 meter, and the distance between the slits (d) is 0.1 mm, the fringe width for red light (with a wavelength of approximately 700 nm) and violet light (with a wavelength of approximately 400 nm) can be calculated as follows:
For red light: $$ w_{\text{red}} = \frac{700 \times 10^{-9} \text{m} \times 1 \text{m}}{0.1 \times 10^{-3} \text{m}} = 7 \times 10^{-3} \text{m} = 7 \text{mm} $$
For violet light: $$ w_{\text{violet}} = \frac{400 \times 10^{-9} \text{m} \times 1 \text{m}}{0.1 \times 10^{-3} \text{m}} = 4 \times 10^{-3} \text{m} = 4 \text{mm} $$
This example illustrates that the fringe width for red light is wider than that for violet light.
Conclusion
YDSE with white light provides a colorful demonstration of the wave nature of light and the principle of superposition. It shows that different wavelengths interfere differently, resulting in a complex pattern of colored fringes. Understanding this experiment is crucial for students and researchers studying wave optics and the behavior of light.