# Geometrical Optics: Explaining the Effects of Small Wavelengths

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• Anish Joshi
In summary: The wavelength is negligible compared to the size of the object because the size of the object is much smaller than the wavelength of light.
Anish Joshi
TL;DR Summary
Read that Ray Optics explains reflection, refraction, formation of shadows, as the wavelength of light is negligible compared to day-to-day objects. Want to understand why Exactly?
The reason Geometrical optics works in case of formation of shadows, reflection and rarefaction is that the wavelength of light is much smaller compared to the reflecting/refracting surfaces as well as shadow causing objects that we use in day-to-day life.

I understand how the wavelength is negligible compared to the size of the object. But I want to understand the mechnaism - why and how does the small wavelength matter here?

First question here, so I apologize if there are any mistakes!

curious_mind
OK, then you'll want to study "Diffraction" which describes how waves propagate through/past restrictions (like the diameter of a lens). You can also study "Huygens Principle". Also look for videos of diffraction of water waves in a wave tank. That's classically very similar to what light does.

Basically, shadows (or light beams) always have fuzzy edges. If the object is small enough all you get is fuzz. If you have a big object, no one cares about a relatively small amount of fuzziness at the edges.

Anish Joshi
Ray optics can be derived from wave optics (i.e., Maxwell's equations) by doing the so-called eikonal approximation (also known as WKB approximation in the context of quantum-mechanical wave mechanics). A good treatment can be found in Sommerfeld, Lectures on Theoretical Physics, vol. 4 (Optics).

curious_mind and Anish Joshi
Anish Joshi said:
TL;DR Summary:

I understand how the wavelength is negligible compared to the size of the object. But I want to understand the mechnaism - why and how does the small wavelength matter here?
To understand an effect of using a shorter wavelength, consider a parabolic reflector in a 1m diameter searchlight. If we can use a very tiny light source, such as a carbon arc, we can obtain a beam which is almost parallel - it is mainly controlled by the geometry and the ray diagram. But now use the same reflector for microwaves, wavelength say 3 cm. The beam now widens to approx 2 degrees. If we increase the wavelength to 30cm it now becomes 20 degrees. When we move a detector away from the axis of the beam, we lose signal because there is a phase error in the radiation from opposite sides of the reflector. When the wavelength is short, this phase error is greater for a given angle off beam. At the longer wavelengths, the geometry no longer gives a reliable answer for the beamwidth.

Anish Joshi

## 1. What is geometrical optics?

Geometrical optics is a branch of optics that studies the behavior of light as it travels in a straight line, without considering its wave nature. It explains how light interacts with objects and how it is reflected, refracted, and absorbed.

## 2. What are small wavelengths in geometrical optics?

In geometrical optics, small wavelengths refer to light with a wavelength that is much smaller than the size of an object or aperture it interacts with. This is typically the case when the size of the object or aperture is in the same range as the wavelength of the light.

## 3. How do small wavelengths affect the behavior of light?

Small wavelengths can cause diffraction effects, where light bends and spreads out as it passes through small openings or around objects. This can also result in interference patterns, where light waves interact with each other and either amplify or cancel out. These effects are not accounted for in geometrical optics.

## 4. What is the significance of understanding small wavelengths in geometrical optics?

Understanding small wavelengths is important for accurately predicting the behavior of light in certain situations, such as when dealing with small objects or apertures. It also helps in developing more precise optical instruments and technologies.

## 5. How does geometrical optics differ from other branches of optics?

Geometrical optics differs from other branches of optics, such as physical optics and quantum optics, in that it does not consider the wave nature of light. Instead, it focuses on the ray model of light, which simplifies the study of light in certain situations but may not fully explain its behavior in others.

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