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# Chapter 20: Geometric Optics

Difficulty Level: At Grade Created by: CK-12

Light refracted through water.

Optics is the study of light.  Geometric optics is the classical science of mirrors, glass, and lenses.  It explains how light bends in water, and how images are formed in mirrors, telescopes, microscopes, and other devices.

Chapter Outline

### Chapter Summary

1. The law of reflection states that the angle of incidence is equal to the angle of reflection θi=θr\begin{align*}\theta_i=\theta_r\end{align*}

The incident ray, the reflected ray and the normal are also coplanar.

2. For the object distance, do\begin{align*}d_o\end{align*} the image distance di\begin{align*}d_i\end{align*}, and the focal length f\begin{align*}f\end{align*}, both the mirror equation and thin lens equation is 1do+1di=1f\begin{align*}\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}\end{align*}

3. For spherical mirrors, f=r2\begin{align*}f=\frac{r}{2}\end{align*}

4. The lateral magnification m\begin{align*}m\end{align*} of an object is defined as the ratio of the image height hi\begin{align*}h_i\end{align*} of the object to the actual height ho\begin{align*}h_o\end{align*} of the object, and is equal to the negative of the ratio of the image distance di\begin{align*}d_i\end{align*} to the object distance do\begin{align*}d_o\end{align*}

m=hiho=dido\begin{align*}m=\frac{h_i}{h_o}=-\frac{d_i}{d_o}\end{align*}

5. We define the ratio of the speed of light through vacuum c\begin{align*}c\end{align*} to the speed of the light through a particular medium v\begin{align*}v\end{align*} as the index of refraction n\begin{align*}n\end{align*}

n=cv\begin{align*}n=\frac{c}{v}\end{align*}

Since c>v\begin{align*}c > v\end{align*}, the index of refraction is always greater than 1 when traveling through any medium other than vacuum.

6. Snell’s law can be defined in terms of the indices of refraction n\begin{align*}n\end{align*} or the speeds of light in the two media. It expresses the relationship between the angle of incidence θ1\begin{align*}\theta_1\end{align*} and the angle of refraction θ2\begin{align*}\theta_2\end{align*} at the interface of two media.

n1sinθ1=n2sinθ2\begin{align*}n_1 \sin \theta_1=n_2 \sin \theta_2\end{align*}

The index of refraction n1\begin{align*}n_1\end{align*} is the medium from which light originates and n2\begin{align*}n_2\end{align*} is the index of refraction of the medium to which light passes. Angle θ1\begin{align*}\theta_1\end{align*} is measured with respect to the normal at the interface of medium 1 and angle θ2\begin{align*}\theta_2\end{align*} is measured with respect to the (same) normal at the interface of medium 2. Snell’s law can be expressed in terms of the velocities of light in the respective media as

v2sinθ1=v1sinθ2\begin{align*}v_2 \sin \theta_1=v_1 \sin \theta_2\end{align*}

where v1\begin{align*}v_1\end{align*} is the speed of the light in medium 1 and v2\begin{align*}v_2\end{align*} is the speed of light in medium 2.

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Jan 13, 2016