Properties of Curved Mirrors and Lenses

Concave Mirror

Convex Mirror

LENSES

Converging Diverging

F F

CONVERGING LENS

Ray parallel to axis through F

Ray through F parallel to axis

Ray through center of lens no bending

Diverging Lens – smaller virtual image inside of F

Mirror & Lens Equations

1 1 1-- + -- = --do di f

di POSITIVE for REAL image NEGATIVE for VIRTUAL image

f POSITIVE for Concave Mirror CONVERGING lens NEGATIVE for Convex Mirror DIVERGING lens

Si - di

M = -- = -- So do

M = magnification

Si = size of image

So = size of object

beyond 2F

@ 2F

between 2F & F

inside of F

@ F

Concave Mirror & Converging Lens

Object Location

Image Location

Image Type

Image Size

beyond 2F (C)

@ 2F (C)

between F & 2F (C)

@ F

inside F

Object Location

Image Location

Image Type

Image Size

beyond 2F (C)

between F & 2F (C)

real smaller

@ 2F (C) @ 2F (C) real same

between F & 2F (C)

beyond 2F (C)

real larger

@ F no image ------------ ------------

inside F Behind mirror;

same side lens

virtual larger

Convex Mirror; Diverging Lensobject @ any location

virtual image, smaller

Plane Mirrorobject @ any location

virtual image, same size