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# 2: Geometric Optics and Image Formation

This chapter introduces the major ideas of geometric optics, which describe the formation of images due to reflection and refraction. It is called “geometric” optics because the images can be characterized using geometric constructions, such as ray diagrams. We have seen that visible light is an electromagnetic wave; however, its wave nature becomes evident only when light interacts with objects with dimensions comparable to the wavelength (about 500 nm for visible light). Therefore, the laws of geometric optics only apply to light interacting with objects much larger than the wavelength of the light.

• 2.0: Prelude to Geometric Optics and Image Formation
loud Gate is a public sculpture by Anish Kapoor located in Millennium Park in Chicago. Its stainless steel plates reflect and distort images around it, including the Chicago skyline. Dedicated in 2006, it has become a popular tourist attraction, illustrating how art can use the principles of physical optics to startle and entertain.
• 2.1: Images Formed by Plane Mirrors
The law of reflection tells us that the angle of incidence is the same as the angle of reflection. A plane mirror always forms a virtual image (behind the mirror). The image and object are the same distance from a flat mirror, the image size is the same as the object size, and the image is upright.
• 2.2: Spherical Mirrors
Spherical mirrors may be concave (converging) or convex (diverging). The focal length of a spherical mirror is one-half of its radius of curvature: $$f = \frac{R}{2}$$. The mirror equation and ray tracing allow you to give a complete description of an image formed by a spherical mirror. Spherical aberration occurs for spherical mirrors but not parabolic mirrors; comatic aberration occurs for both types of mirrors.
• 2.3: Images Formed by Refraction
When an object is observed through a plane interface between two media, then it appears at an apparent distance hi that differs from the actual distance $$h_0$$: $$h_i = \left(\frac{n_2}{n_1}\right)h_0$$. An image is formed by the refraction of light at a spherical interface between two media of indices of refraction n1 and $$n_2$$. Image distance depends on the radius of curvature of the interface, location of the object, and the indices of refraction of the media.
• 2.4: Thin Lenses
Two types of lenses are possible: converging and diverging. A lens that causes light rays to bend toward (away from) its optical axis is a converging (diverging) lens. By the end of this section, you will be able to use ray diagrams to locate and describe the image formed by a lens and employ the thin-lens equation to describe and locate the image formed by a lens.
• 2.5: The Eye
The human eye is perhaps the most interesting and important of all optical instruments. Our eyes perform a vast number of functions: They allow us to sense direction, movement, colors, and distance. In this section, we explore the geometric optics of the eye.
• 2.6: The Camera
Cameras use combinations of lenses to create an image for recording. By the end of this section, you will be able to: Describe the optics of a camera. Characterize the image created by a camera.
• 2.7: The Simple Magnifier
A simple magnifier is a converging lens and produces a magnified virtual image of an object located within the focal length of the lens. The magnification of an image when observed by the eye is the angular magnification M, which is defined by the ratio of the angle $$θ_{image}$$ subtended by the image to the angle $$θ_{object}$$ subtended by the object.
• 2.8: Microscopes and Telescopes
Many optical devices contain more than a single lens or mirror. These are analyzed by considering each element sequentially. The image formed by the first is the object for the second, and so on. The same ray-tracing and thin-lens techniques developed in the previous sections apply to each lens element. The overall magnification of a multiple-element system is the product of the linear magnifications of its individual elements times the angular magnification of the eyepiece.
• 2.A: Geometric Optics and Image Formation (Answers)
• 2.E: Geometric Optics and Image Formation (Exercises)
• 2.S: Geometric Optics and Image Formation (Summary)

Thumbnail: Rays reflected by a convex spherical mirror: Incident rays of light parallel to the optical axis are reflected from a convex spherical mirror and seem to originate from a well-defined focal point at focal distance f on the opposite side of the mirror. The focal point is virtual because no real rays pass through it.

### Contributors

• Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).