phys 120: lenses, refraction, reflection, and other stuff: equations and concepts

index of refraction equation (and the constant)

n=c/v (c is the speed of light in a vacuum and = 3.00×10^8

Snell’s law, which relates the index of refraction and angle of incidence of one medium to another

What is the critical angle, and what does it represent?

the critical angle: the angle of incidence at which the angle of refraction is 90 degrees. if this angle is exceeded, then there is total internal reflection. Sin@c=n2/n1

NOTE: n1 must be greater than n2, meaning that total internal reflection can only happen when it goes from a more dense medium to a less dense medium

relationship between reflected ray and incident ray on a flat surface

@i=@r

equations for focal length

P = 1/f = 1/di + 1/do

f = 1/2(R) OR f = -1/2(R), for use with a convex mirror

rules for drawing ray: CONCAVE MIRROR

ray 1: leaves parallel to principal axis, reflects off mirror, and passes through focal point

ray 2: passes through foal point, reflects off mirror, and emerges parallel to axis

ray 3: travels along a line that passes through the center of curvature, C

rules for drawing rays: CONVEX MIRRORS

Ray 1: initially parallel to principal axis, reflects, and emerges in a way that seems like it came from the focal point on the other side

ray 2: heads towards the focal point on the other side, and emerges parallel to axis

ray 3: travel towards center of curvature, C, and reflects back on itself

CONVEX mirrors produce a predictable image:

located behind the convex mirror

a virtual image

an upright image

reduced in size (i.e., smaller than the object)

sign conventions for MIRRORS: di, do, f, and m

f is positive for a concave lens (usually) and negative for a convex lens

di is positive if in front of mirror, and - if behind mirror

m is + for an upright image, and - for an inverted image

rules for drawing rays: CONVEX LENS

ray 1: leaves object parallel to axis, refracts,a ND goes through f on the other side

ray 2: goes through f on the same side, refracts, and goes parallel

ray 3: goes through midpoint of lens unrefracted

rules for drawing rays: CONCAVE LENS

ray 1: parallel to axis, refracts in a way that makes it seem that it came from f in the front

ray 2: goes towards f on the other side, and emerges parallel to axis

ray 3: goes through midpoint of lens unrefracted