Does Light Pass Through a Slit Unaltered When Wavelength Equals Slit Width?

[Alice-Shallom]

Hi,
I need help with the following:

Prove that if the wavelength of light is equal to or greater than the width of a slit, light striking the slit perpendicularly passes through without forming any dark interference bands.

 

[Tony Zalles]

I think our AP Physics talked about something like that towards the end of the year...but by that time Senioritis was in full effect...lol

 

[M98Ranger]

Single-slit diffraction is a phenomenon that occurs when light passes through a narrow slit and spreads out into a pattern of bright and dark fringes. The diffraction pattern is a result of the wave nature of light, as the light waves bend and interfere with each other as they pass through the slit. However, it has been observed that when the wavelength of light is equal to or greater than the width of the slit, the diffraction pattern disappears and the light passes through the slit without forming any dark interference bands.

To prove this, we can use the principle of Huygens-Fresnel diffraction, which states that every point on a wavefront can be considered as a source of secondary waves. These secondary waves interfere with each other to produce the overall diffraction pattern.

In the case of a single slit, the secondary waves from different points on the slit interfere with each other to produce a diffraction pattern. This pattern is characterized by a central bright fringe, flanked by a series of dark fringes on either side.

Now, let us consider the scenario where the wavelength of light is equal to or greater than the width of the slit. In this case, the width of the slit is relatively small compared to the wavelength of light, and the secondary waves from different points on the slit interfere constructively with each other. As a result, the intensity of light at the central bright fringe is significantly higher than the intensity at the dark fringes. This means that the dark fringes are not visible, and the light appears to pass through the slit without any interference pattern.

On the other hand, if the wavelength of light is smaller than the width of the slit, the secondary waves from different points on the slit interfere destructively, resulting in a diffraction pattern with distinct dark fringes.

In conclusion, when the wavelength of light is equal to or greater than the width of the slit, the diffraction pattern disappears, and the light passes through the slit without any interference bands. This can be explained by the principle of Huygens-Fresnel diffraction, where the interference of secondary waves from different points on the slit results in a constructive interference at the central bright fringe, making the dark fringes invisible.