Plane MirrorsThe image formed by a plane mirror is upright, identical in size to the object, and as far behind the mirror as the object is in front of it.
Plane Mirrors
The magnification is given by:
For a plane mirror, M = +1.
Spherical MirrorsA spherical mirror is a section of a sphere. It may be concave or convex.
Spherical MirrorsA concave mirror (left) focuses incoming parallel rays at the focal point. A convex mirror bends incoming parallel rays outward, as though they came from a focal point behind the mirror.
Spherical MirrorsImages formed by spherical mirrors may be found by using the parallel, chief, and focal rays.
Spherical Mirrors
For a concave mirror, the type of image formed depends on the position of the object.
Spherical Mirrors
If the object is at the focal point, there is no image.
Spherical Mirrors
The spherical-mirror equation is valid for any object position:
Sign conventions for spherical mirrors are given on the next slide.
Spherical Mirrors
Spherical Mirrors
The magnification is given by:
Spherical Mirrors
For a convex mirror the process is similar, but the image will always be virtual.
Spherical Mirrors
Spherical aberration occurs because rays far from the mirror axis do not go through the focal point.
LensesSpherical lenses have surfaces defined by two spheres.
Lenses
A converging lens brings incoming rays together at the focal point.
Lenses
The rays emerging from a diverging lens appear to have come from a single focal point.
Lenses
Both converging and diverging lenses come in a variety of shapes.
LensesImages formed by lenses can be found just as mirror images were found. The first two rays:
LensesLocating and confirming the image:
Lenses
The type of image formed by a converging lens depends on the position of the object. For a distant object:
LensesFor an object closer than the focal point:
Lenses
Lenses
The thin-lens equation:
Magnification:
LensesA diverging lens always forms a virtual image.
LensesIn a multi-lens system, the image formed by the first lens becomes the object for the next.
The Lens Maker’s Equation
We start with sign conventions:
23.4 The Lens Maker’s Equation
In general, each lens has two radii of curvature.
23.4 The Lens Maker’s Equation
This is the lens maker’s equation for a thin lens in air:
The power of a lens may be described using diopters:
Lens AberrationsSpherical aberration occurs when rays far from the axis do not focus at the focal point.
Lens AberrationsChromatic aberration occurs because the index of refraction depends slightly on wavelength, so light of different wavelengths focuses at different points.
Review
• Plane mirrors form virtual, upright, and unmagnified images.
• The object distance is equal to the image distance.
• The lateral magnification factor for all mirrors and lenses is: