Download Thin Lenses Notes

Refraction of Light
n
Index of Refraction:
Wavelength of light in a material:
c
v
(n ≥ 1)
n 
vac
n
Because light travels at different velocities in different materials, light “bends” or refracts at
the interface between two materials.
Snell’s Law:
n1 sin 1  n2 sin  2
- for light traveling from material 1 to material 2
- if n1 < n2, the light is bent “toward” the normal (θ2 < θ1)
- if n1 > n2, the light is bent “away” the normal (θ2 > θ1)
n 
d   d  2 
 n1 
n
Critical Angle:
(n1 > n2)
sin  c  2
n1
- Total Internal Reflection: for angles at the critical angle and bigger, no light is
transmitted into material 2; the light ray just skims along the interface between the two
materials.
Apparent depth:
The index of refraction of a material depends slightly on the wavelength of light. This leads to
dispersion – the spreading of light into its color components. Examples of dispersion of light:
prisms and rainbows.
Lenses
To understand thin lenses (and mirrors) and the images they form, we trace the paths of light
rays from the object to the lens (or mirror) and then on to where the image is formed. An
image is formed where the light rays all “intersect”. For a real image, the light rays really do
intersect. For an imaginary image, the light rays do not actually intersect because they are
diverging. We trace the actual light rays back through the lens to see where they appear to
come from – this is the location of the imaginary image.
In this class, to minimize confusion, we always work from left to right. So a real object is to
the left of the lens. In real life, of course light can go left to right or right to left through a lens.
Converging Lens
Object Placement
Image Type
Image Size
Beyond 2F
Between 2F & F
Real
Real
Reduced
Enlarged
Image
Orientation
Inverted
Inverted
Between F and
Lens
Virtual
Enlarged
Upright
Example
Camera
Film
projector
Magnifying
glass
Diverging Lens
Object Placement
Anywhere
Image Location/Type
Virtual
Image Size
Reduced
Thin Lens Equation:
1
1
1


do di
f
Magnification Equation:
m
Image Orientation
Upright
hi
d
 i
ho
do
Sign Conventions
- Focal Length
converging lens:
f=+
diverging lens:
f=- Object Distance
object to left of the lens (real object):
do = +
“object” (image from first lens) to right of 2nd lens (virtual object):
- Image Distance
image formed to right of lens (real image): di = +
image formed to left of lens (virtual image): di = - Magnification
image is upright: m = +
image is inverted: m = Compound lens equation (lenses touching each other):
do = -
1
1
1


f1 f 2
f
Lenses in combination but not touching: with a multiple lens system, you apply the thin lens
equation to each lens separately to find the location of the final image. The image from the
first lens serves as the object for the second lens.