Summary

• 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.

• Spherical mirrors may be concave (converging) or convex (diverging).
• The focal length of a spherical mirror is one-half of its radius of curvature: $f=R\text{/}2$.
• 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.

This section explains how a single refracting interface forms images.

• When an object is observed through a plane interface between two media, then it appears at an apparent distance $h_{\text{i}}$ that differs from the actual distance $h_{\text{o}}$: $h_{\text{i}}=(n_2\text{/}{n}_1)h_{\text{o}}$.
• An image is formed by the refraction of light at a spherical interface between two media of indices of refraction $n_1$ 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.

• 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.
• For a converging lens, the focal point is where the converging light rays cross; for a diverging lens, the focal point is the point from which the diverging light rays appear to originate.
• The distance from the center of a thin lens to its focal point is called the focal length f.
• Ray tracing is a geometric technique to determine the paths taken by light rays through thin lenses.
• A real image can be projected onto a screen.
• A virtual image cannot be projected onto a screen.
• A converging lens forms either real or virtual images, depending on the object location; a diverging lens forms only virtual images.

• Image formation by the eye is adequately described by the thin-lens equation.
• The eye produces a real image on the retina by adjusting its focal length in a process called accommodation.
• Nearsightedness, or myopia, is the inability to see far objects and is corrected with a diverging lens to reduce the optical power of the eye.
• Farsightedness, or hyperopia, is the inability to see near objects and is corrected with a converging lens to increase the optical power of the eye.
• In myopia and hyperopia, the corrective lenses produce images at distances that fall between the person’s near and far points so that images can be seen clearly.

• Cameras use combinations of lenses to create an image for recording.
• Digital photography is based on charge-coupled devices (CCDs) that break an image into tiny “pixels” that can be converted into electronic signals.

• A simple magnifier is a converging lens and produces a magnified virtual image of an object located within the focal length of the lens.
• Angular magnification accounts for magnification of an image created by a magnifier. It is equal to the ratio of the angle subtended by the image to that subtended by the object when the object is observed by the unaided eye.
• Angular magnification is greater for magnifying lenses with smaller focal lengths.
• Simple magnifiers can produce as great as tenfold ($10\times$) magnification.

• 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. For a two-element system with an objective and an eyepiece, this is
  $$M=m^{\text{obj}}{M}^{\text{eye}}.$$

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  where $m^{\text{obj}}$ is the linear magnification of the objective and $M^{\text{eye}}$ is the angular magnification of the eyepiece.
• The microscope is a multiple-element system that contains more than a single lens or mirror. It allows us to see detail that we could not to see with the unaided eye. Both the eyepiece and objective contribute to the magnification. The magnification of a compound microscope with the image at infinity is
  $$M_{\text{net}}=\text{−}\frac{(16\text{cm})(25\text{cm})}{f^{\text{obj}}{f}^{\text{eye}}}.$$

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  In this equation, 16 cm is the standardized distance between the image-side focal point of the objective lens and the object-side focal point of the eyepiece, 25 cm is the normal near point distance, $f^{\text{obj}}$ and $f^{\text{eye}}$ are the focal distances for the objective lens and the eyepiece, respectively.
• Simple telescopes can be made with two lenses. They are used for viewing objects at large distances.
• The angular magnification M for a telescope is given by
  $$M=\text{−}\frac{f^{\text{obj}}}{f^{\text{eye}}},$$

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  where $f^{\text{obj}}$ and $f^{\text{eye}}$ are the focal lengths of the objective lens and the eyepiece, respectively.