ni
nr
θr
θi
Snell's Law: ni sin(θi) = nr sin(θr)
Note:
a) if θi = 0°, then θr = 0°
b) if nr > ni, then θr < θi
Typical refractive indices:
air, n = 1.0
glass, n = 1.3
water, n = 1.3
Example:
ni = 1.0, nr = 1.3, θi = 45°, what is θr?
sin(45°) = 0.707 so ...
sin(θr) = (1.0) (0.707) / (1.3) = 0.54 so ...
θr = arcsin(0.54) = 32.7°
Try at home:
ni = 1.3, nr = 0.9, θi = 30°, what is θr?
Light coming
from a point very
far away (e.g. a
star)
f1
Light coming
from a point very
far away (e.g. a
star)
f2
The focal length is a property of a lens. It is the
distance at which light from a point source very far
away is focused. The focal length of the top lens
shown above is f1. The focal length of the bottom
lens is f2. In general, fatter lenses have shorter focal
lengths.
The power of a lens is measured in diopters. The
number of diopters is given by D = 1/f, where f is the
focal length of the lens in meters.
do
di
The lensmaker's formula relates the distance of an object
from a lens (do) to the distance of the image from the lens (di).
The lensmaker's formula is : 1/do + 1/di = 1/f where f is the focal
length of the lens.
Note:
If the focal length increases and the object is at the same
distance, then the image will be further away from the lens.
If the focal length is fixed and we move the object closer
to the lens, then the image will be further from the lens.
When the distance to the object is infinite, then the distance
to the image is just the focal length, as shown below.
do = infinity
di = f