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# Chapter 21: Physical Optics

Difficulty Level: At Grade Created by: CK-12

A rainbow is an example of physical optics, where light shows properties like a wave.

Physical optics, also called wave optics, is the study of phenomena where light behaves like a classical wave and not like a ray or particle.  A rainbow is a classic example of this, where different colors of light separate based on their wavelength.  This also includes dispersion, the double-slit experiment showing interference, thin films, and polarization.

Chapter Outline

### Chapter Summary

1. When white light passes through a glass prism, a rainbow-like array of colors, called the visible spectrum, exits the prism. The spreading of light in this manner is called dispersion.

2. Dispersion is caused by the fact that the speed of light in a medium other than vacuum depends on its frequency (color).

3. Red light is refracted the least and violet light refracted the most.

4. Light with wavelength λ\begin{align*}\lambda\end{align*} in air, has a wavelength λn=λn\begin{align*}\lambda_n=\frac{\lambda}{n}\end{align*} in a medium of refractive index n\begin{align*}n\end{align*}.

5a. Constructive interference condition for a double-slit is arrangement given by the equation

dsinθ=mλ, m=0,1,2,\begin{align*}d \sin \theta = m \lambda, \ m=0,1,2, \ldots\end{align*}

where d\begin{align*}d\end{align*} is the distance between the slits, θ\begin{align*}\theta\end{align*} is the diffracting angle, m\begin{align*}m\end{align*} is the order and λ\begin{align*}\lambda\end{align*} is the wavelength of the light.

5b. Destructive interference condition for a double-slit arrangement is given by the equation

dsinθ=(m+12)λ, m=0,1,2,\begin{align*}d \sin \theta = \left(m+\frac{1}{2}\right) \lambda, \ m=0,1,2, \ldots\end{align*}

6a. Constructive interference for a thin film of thickness d\begin{align*}d\end{align*} and wavelength of light λ\begin{align*}\lambda\end{align*}(in the film) when there is no effective phase change, is given by the equation

2d=mλ, m=0,1,2,\begin{align*}2d = m \lambda, \ m=0,1,2,\ldots\end{align*}

6b. Destructive interference for thin films when there is no effective phase change is

2d=(m+12)λ, m=0,1,2,\begin{align*}2d = \left(m+\frac{1}{2}\right) \lambda, \ m=0,1,2,\ldots\end{align*}

7a. When a beam of light is reflected from a medium with a greater index of refraction than the medium in which it travels, it undergoes a phase change of 180\begin{align*}180^{\circ}\end{align*} upon reflection. The condition for a constructive interference when a phase change of 180\begin{align*}180^{\circ}\end{align*} occurs is given by the equation

2d=(m+12)λ, m=0,1,2,\begin{align*}2d = \left(m+\frac{1}{2}\right) \lambda, \ m=0,1,2,\ldots\end{align*}

7b. The condition for a destructive interference when a phase change of 180\begin{align*}180^{\circ}\end{align*} occurs is given by the equation

2d=mλ, m=0,1,2,\begin{align*}2d = m \lambda, \ m=0,1,2,\ldots\end{align*}

8. Polarization is a property associated with transverse waves – most typically, electromagnetic waves. Light that is polarized has electric field vibrations in only one plane. A “polarizer” filters out all of the vibrations in a transverse wave that are not in a particular plane. A polarizer that permits vertical vibrations to pass has vertical axis of polarization. A polarizer that permits horizontal vibrations to pass has horizontal axis of polarization. Light can be polarized by transmission or reflection.

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Date Created:
Jan 13, 2016