Why Do Longer Wavelengths Diffract More Than Shorter Wavelengths?

[Yuqing]

I've been told that longer wavelengths are able to diffract more than short wavelengths. The hyperphysics page on sound wave diffraction also states this fact. Nothing I've read have explained why exactly longer wavelengths are able to diffract more than shorter wavelengths, so that's my question here.

Also, the hyperphysics page also mentions about wavelengths and their ability to transfer information. Electron microscopes are able to produce images of smaller items because the wavelength of the electron is smaller than visible light. How does a shorter wavelength help to produce a sharper image?

 

[buffordboy23]

I've been told that longer wavelengths are able to diffract more than short wavelengths. The hyperphysics page on sound wave diffraction also states this fact. Nothing I've read have explained why exactly longer wavelengths are able to diffract more than shorter wavelengths, so that's my question here.

Have you seen the derivation for locating the minima in a single-slit diffraction experiment? What is the equation? Let m = 1, and then solve for theta, which is the angle from the central axis to the point at the first minima.

 

[nlightner]

I can confirm that longer wavelengths do indeed diffract more than shorter wavelengths. This is due to the relationship between wavelength and the size of the diffracting object. According to the Huygens-Fresnel principle, when a wave passes through an opening or around an obstacle, the wavefronts become curved and spread out. The amount of diffraction is directly proportional to the size of the obstacle or opening and inversely proportional to the wavelength of the wave. Therefore, longer wavelengths, which have a larger size, will diffract more than shorter wavelengths.

In terms of electron microscopes, the shorter wavelength of electrons compared to visible light allows for a higher resolution image to be produced. This is because the resolution of an image is limited by the size of the wavelength of the light or particles used to produce it. The smaller the wavelength, the smaller the details that can be resolved. This is why electron microscopes, with their shorter electron wavelengths, can produce sharper and more detailed images compared to visible light microscopes.

Additionally, the shorter wavelength of electrons also allows them to interact more strongly with the sample being imaged, providing more contrast and detail in the resulting image. This is due to the fact that electrons have a higher energy and shorter wavelength compared to visible light, making them more sensitive to small variations in the sample's composition and structure.

In summary, the relationship between wavelength and diffraction is based on the size of the diffracting object, with longer wavelengths diffracting more due to their larger size. In the case of electron microscopes, the shorter wavelength of electrons allows for higher resolution and more detailed images, as well as stronger interactions with the sample being imaged.