Geometric Optics
Light travels in straight lines (rays) unless the light
encounters some change in medium.
When the light reaches a change in medium two
actions my occur.
reflection
refraction
Sometimes both occur
(Remember, light travels as a wave and these are wave properties.)
examples:
light reflecting off of a mirror
the reflection of a street light off of a puddle
light refracting as it travels through a prism.
What constitutes a change in medium?
Light travels at different speeds through different
materials.
This is determined by the index of refraction (n) of the
material.
n = c/v
c is speed of light in a vacuum
v is the speed of light in the medium
Whenever light encounters a boundary, the index of
refraction changes, and reflection and refraction may
take place.
Common values of n
air n = 1.000293 water n = 1.3 glass n = 1.5
example of reflection
Law of reflection
When light reflects off of a surface, the angle the
incident light makes to a line perpendicular
(normal line) to the surface is the same angle
the reflected makes to the normal line.
angle of incidence ( i) = angle of reflection ( r)
normal line
incident ray
reflected ray
i
r
surface
example of refraction
When light goes from air to water it refracts (bends).
The picture on the right shows why the straw
appears bent.
Example of reflection and refraction occurring.
Quite often light undergoes both reflection and refraction.
Here light passes from air to glass then back to air.
incident ray
reflected ray
air
glass
refracted ray
air
Example of reflection and refraction occurring.
Here is a nicer picture.
Law of refraction
Snell’s Law: n1 sin 1 = n2 sin 2
If light goes from higher n to lower n, the light
bends away from the normal.
If light goes from lower n to higher n, the light
bends closer to the normal.
Nice webpage to play with:
http://www.ps.missouri.edu/rickspage/refract/re
fraction.html
Application of refraction
Lenses:
By taking advantage of the bending of light as it
passes through a lens, people can control the path
that light takes.
two types of lenses: converging lens, diverging lens
Converging lens takes rays and focuses them to a
point.
Diverging lens causes the rays to spread out.
Converging lens.
Ray tracing rules
1) If ray comes from parallel to axis, after being refracted, it will
pass through the focal point on the opposite side of the lens.
2) If ray is drawn through the center of the lens, it keeps going
straight.
3) If ray is drawn through the focal on the same side of the
object, after going through the lens, it will be parallel to the
principle axis.
1
2
3
Diverging rays cause the incoming rays to
spread out after passing through the lens.
The rules for ray tracing for diverging lenses are similar to those for
a converging lens.
1) If a ray comes from parallel to the central axis, it bends away, as
if it came from the focal point on the initial side of the lens.
2) If ray is drawn through the center of the lens, it keeps going straight.
3) If a ray would have gone through the focal point on the opposite
side of the lens, it leaves the lens parallel to the central axis.
Mirrors use the Law of Reflection to
redirect light.
For a flat mirror, the reflection will be just like
the object except reverses laterally.
For spherical mirrors, the image can be either
enlarged or reduced, and upright or inverted
The law of reflection still hold, but the
rounded surface of the mirror produces the
different results.
Ray tracing for Spherical mirrors
1) Rays drawn parallel to principle axis are
reflected through the focal point.
2) Rays drawn through focal point are reflected
parallel to principle axis.
3) Ray drawn through center of curvature
(point C) get reflected back on itself.
4) Also can see that a ray incident at the center
of the mirror is reflected at an equal angle.
Play around with website to see what happens
when you move the object around.
http://physics.bu.edu/~duffy/semester2/c25_sp
herical.htm
http://www.physics.brocku.ca/Courses/1P22_Cr
andles/applets/Mirrors/