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Chapter 20: Geometric Optics

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Credit: Petr Kratochvil
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Light refracted through water. [Figure1]

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 \theta_i=\theta_r

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

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

3. For spherical mirrors, f=\frac{r}{2}

4. The lateral magnification m of an object is defined as the ratio of the image height h_i of the object to the actual height h_o of the object, and is equal to the negative of the ratio of the image distance d_i to the object distance d_o

m=\frac{h_i}{h_o}=-\frac{d_i}{d_o}

5. We define the ratio of the speed of light through vacuum c to the speed of the light through a particular medium v as the index of refraction n

n=\frac{c}{v}

Since c > v, 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 or the speeds of light in the two media. It expresses the relationship between the angle of incidence \theta_1 and the angle of refraction \theta_2 at the interface of two media.

n_1 \sin \theta_1=n_2 \sin \theta_2

The index of refraction n_1 is the medium from which light originates and n_2 is the index of refraction of the medium to which light passes. Angle \theta_1 is measured with respect to the normal at the interface of medium 1 and angle \theta_2 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

v_2 \sin \theta_1=v_1 \sin \theta_2

where v_1 is the speed of the light in medium 1 and v_2 is the speed of light in medium 2.

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Date Created:

Jun 27, 2013

Last Modified:

May 22, 2014
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