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This course is designed for engineers. This subject is compiled of physical applications and concepts. This lecture includes: Plane Mirrors, Spherical Mirrors, Concave and Convex Mirrors, Mirrors, Images Formed By Plane Mirrors, Plane Mirrors, Virtual Images, Center of Curvature, Radius of Curvature, Principal Axis
Typology: Slides
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Today’s agenda:
Plane Mirrors. You must be able to draw ray diagrams for plane mirrors, and be able to calculate image and object heights, distances, and magnifications.
Spherical Mirrors: concave and convex mirrors. You must understand the differences between these two kinds of mirrors, be able to draw ray diagrams for both kinds of mirrors, and be able to solve the mirror equation for both kinds of mirrors.
Plane mirrors form virtual images; no light actually comes from the image. The solid red rays show the actual light path after reflection; the dashed black rays show the perceived light path.
Images Formed by Plane Mirrors
s s’
Example: how tall must a full-length mirror be?
A light ray from the top of your head reflects directly back from the top of the mirror.
s s’
y/
y/
To reach your eye, a light ray from your foot must reflect halfway up the mirror (because I = R = ).
Example: where is the image located (top view)?
Example: distant object in a small mirror.
Find some similar triangles! (Only one is fully shown in the figure.)
Images Formed by Spherical Mirrors
Spherical mirrors are made from polished sections cut from a spherical surface.
The center of curvature , C, is the center of the sphere, of which the mirror is a section.
Of course, you don’t really make these mirrors by cutting out part of a sphere of glass.
The radius of curvature , R, is the radius of the sphere, or the distance from V to C.
Paraxial rays are parallel to the principal axis of the mirror (from an object infinitely far away). Reflected paraxial rays pass through a common point known as the focal point F.
The focal length f is the distance from P to F. Your text shows that f = R/2.
f
If the mirror is small compared to its radius of curvature, or the object being imaged is close to the principal axis, then the rays essentially all focus at a single point.
We will assume mirrors with large radii of curvature and objects close to the principal axis.
In ―real life‖ you would minimize aberration by using a parabolic mirror.
Concave and Convex Mirrors
There are two kinds of spherical mirrors: concave and convex.
concave convex
Ray Diagrams for Mirrors
We can use three ― principal rays ‖ to construct images. In this example, the object is ―outside‖ of F.
Ray 1 is parallel to the axis and reflects through F.
Ray 2 passes through F before reflecting parallel to the axis.
Ray 3 passes through C and reflects back on itself.
A fourth principal ray is the one directed at the vertex V.
