MIRRORSGeometric Optics

Mirror

- any surface that is smooth enough to produce regular or specular reflection

Types of Mirrors1. Plane Mirrors – mirrors with flat surfaces2. Spherical Mirrors – mirrors with curve

surfaces

Images Formed With Mirrors1. Real Image - formed in front of a mirror;

it can be projected on a screen; it is always inverted

2. Virtual Image - it is always found at the “back” of the mirror; it can not be focused or projected on a screen; it is always upright

Characteristics of Images Formed in Plane Mirrors

• virtual• upright • same size as the object• same distance from the mirror as the

object in front of the mirror• laterally reversed

Spherical Mirrors

- mirrors with curve surfaces; its surface is taken from the surface of a sphere, hence the name

Types of Spherical Mirrors:1. Concave Spherical Mirrors - the

reflecting surface curves inward in the direction of the incident ray; also called converging mirrors

2. Convex Spherical Mirrors - the reflecting surface curves outward to the incident ray; also called diverging mirrors

Parts of Spherical Mirrors1. center of curvature ( C ) – center of the sphere where the

mirror was taken2. vertex ( V ) – center of the mirror, also called pole of the

mirror 3. principal focus ( F ) – the point where the reflected rays

meet; it is midway between C and V

V Vf f

Parts of Spherical Mirrors4. principal axis – straight line joining C and V, also called

optical axis5. radius of curvature ( R ) – radius of the sphere; distance

between C and V6. focal length ( f ) – distance from C to F or from V to F; is

equal to half of the radius (R)7. aperture – width of the mirror (the blue line)

V Vf f

• fin

Spherical Mirror EquationOPERATIONAL DEFINITION:

1 / f = 1 / p + 1 / q

where:f is the focal lengthp is the object distance from the mirrorq is the image distance from the mirror

Sign Convention:+ for distances measured in front of the mirror- for distances measured behind (back) of the mirror

Mirror Magnification

• Magnification is the ratio of the height of the image to the height of the object.

OPERATIONAL DEFINITION: M = hi / ho

M = q / p

Mirror Equation & Magnification1. An object is located 3cm in front of a concave

mirror whose radius of curvature is 12cm. Find:a. focal length (f) of the mirrorb. distance of the image from the mirror (q)c. the magnification of the mirror (M)d. height (hi)of the image if the object is 2cm tall

2. An object 4.5cm high is placed 50cm in front of a convex mirror with a radius of curvature of 20cm. What is the height of the image?