1. Refraction and Lenses

2. Refraction
A wave is refracted when it “bends” in response to a change in speed.
Moving across a boundary from one medium into another causes a change in the wavelength with a corresponding shift in direction.

3. Index of Refraction Light changes speed (v) as it enters a new medium
In a vacuum the speed of light (c) is 3.0 x 108m/s
The index of refraction (n) of a material is the ratio of the speed of light in a vacuum to the speed of light in the material.
Index of refraction has no units!

4. Refraction
Light slows down and bends toward the normal when entering a more optically dense medium (greater n).
Light speeds up and bends away from the normal when entering a less optically dense medium (smaller n).
Air (n = 1.00)
Glass (n=1.50)
Air (n = 1.00)
Glass (n=1.50)

5. Relationship between angle, velocity, wavelength and index
When the velocity changes it is the wavelength that changes, not the frequency These ratios relate the various characteristics of waves moving between media.

6. Snell’s Law i n = index of refraction for the medium r
normal
incident ray
Air (n=1.00) i
n = index of refraction for the medium
Boundary
refracted ray r
Water (n= 1.33)
Angles are always measured from the normal, never the surface

7. Critical Angle
The angle of incidence that causes the angle of refraction to be 90o
The refracted ray is tangent to
the boundary between mediums
Only possible when going from a
more optically dense (high index of refraction) to less optically dense medium (low index of refraction)
Only possible when light speeds up as it passes through the boundary
n=1
r=900
n=1.5 c

8. Total Internal Reflection
When the angle of incidence exceeds the critical angle, the light does not cross the boundary into the new medium or refract.
All of the light is reflected back into the incident medium according to the Law of Reflection (angle of incidence = angle of reflection)
Application – fiber optic cables

9. Dispersion and Prisms
The index of refraction depends on the wavelength of light so different colors of light bend at different angles.
Shorter wavelengths (blue end of the visible spectrum) bend the most.
A prism separates or disperses white light into the color spectrum as shown above.

10. Wavelength and Frequency of the visible light spectrum

11. Concave Lenses Thicker at the edges than in the center
Parallel rays of light from a far object will refract through the lens and diverge as if they came from the focal point in front.
Concave lenses are also called “diverging lenses”.
Light may come in from either side of lens so there will be a focal point on both sides equal distances from the lens (assuming symmetrical lenses).

12. Convex Lenses Thicker in the center than at the edges
Parallel rays of light from a far object will refract through the lens and converge at the focal point on the other side of the lens.
Convex lenses are “converging lenses”.
Light may come in from either side of lens so there will be a focal point on both sides equal distances from the lens (assuming symmetrical lenses).

13. Calculations f = focal length do = object distance di = image distance
hi = image height
ho = object height
M = magnification

14. Sign conventions Focal length (f) Converging (convex) f = +
Diverging (concave)  f = -
Image distance (di)
di=+ , image is real & on opposite side
do= - , then image is virtual & on same side
Magnification (M)
M = +, image is erect & hi = +
M = - , image is inverted & hi = -

15. Ray Diagram Convex Lens (do>f) Image is real, & inverted
Draw rays from tip of object:
1) parallel, then through primary f
2) through the center of the lens
3) through the front f, then parallel
4) Image is located where the refracted rays converge
Image is real, & inverted
object f
image
f ’

16. Ray Diagram Convex Lens (Inside f) Image is virtual, erect, & larger
Draw 2-3 rays from tip of object:
1) parallel, then through primary f
2) through the center of the lens
3) from f on same side through tip of the object, then parallel
4) Extend the refracted rays back (dashed lines) to locate the image
Ray Diagram
Convex Lens (Inside f)
image
Image is virtual,
erect, & larger f
f ‘
object

17. Ray Diagram Concave Lens Image is virtual, erect, & smaller
Draw 2-3 rays from tip of object & refract at vertical line:
1) parallel, then refracted ray from f on same side of lens
2) through the center of lens
3) to lens along a line that would pass through f on the other side of lens, then parallel
4) Extend refracted rays back (dashed lines) to locate image
concave lens (axis)
object
image f f
Image is virtual,
erect, & smaller

18. Polarizing filters Only allows light in one plane to pass through
Light is reduced by one-half
Sunglasses – polarized vertically, cuts out the horizontal components of light to reduce glare from horizontal surfaces such as sand or water

19. Photoelectric Effect
The emission of electrons from a surface when light of certain frequencies shine on the surface.