2. the change of direction of a ray of light
as it passes obliquely from one medium into
another of different transmission speed
Optical Density of a medium
refers to the speed of
light in that medium.
It does not necessarily
Correspond to the
Mass density of that material.

3. i i > r r Example: light slows down when it passes from air
When light travels from a less dense to
more dense medium (light slows down),
the ray is refracted toward the normal.
Example: light slows down when it passes from air
into water n i
air i
> r
water r

4. i r i < r n Example: light speeds up when passing from
When light travels from a more dense
medium to a less dense medium (light speeds up),
the ray is refracted away from the normal.
Example: light speeds up when passing from
glass into air
air i n r
glass i
< r

5. An object’s ability to decrease the speed of light,
and therefore cause refraction, is given by its
index of refraction. By definition:
the index of refraction of any transparent substance
is equal to the speed of light in a vacuum
divided by
the speed of light in that substance.
n = c / v
n = (3 x 108 m/s) / v

6. The table to the left shows values of the index of refraction for some common substances.
The larger the index of refraction, the slower that light travels through the substance.

7. n1 sin q1 = n2 sin q2 This relationship is known as Snell’s Law. q1 n1
The angles of incidence and refraction are related
in such a way that n = (sin i)/(sin r), where
i = angle of incidence and
r = angle of refraction
whenever light passes from a vacuum
into the substance.
In general, for light passing from medium 1 into medium 2,
n1 sin q1 = n2 sin q2
This relationship is known as Snell’s Law. q1 n1 n2 q2

8. sin qc = 1/n Total Internal Reflection may
occur when light enters a new
medium and speeds up (bends
away from the normal).
Investigate here.
The maximum angle of incidence in which light may enter air from another substance and not undergo total internal refraction is known as the critical angle, and is related to the index of refraction of the substance by:
sin qc = 1/n

9. Click here, here,
and here to view
simulations of Snell’s
Law.
View an analytical derivation
of the geometrical
relationship here.
Investigate total internal reflection here.

10. LENS any transparent object having
two nonparallel curved surfaces or one
plane surface and one curved surface
Converging Lenses - thicker in middle than in the edge
double convex
plano-convex
concavo-convex
These lenses converge light to a real focus.

11. Diverging Lenses - thicker at edge than in middle
double concave
plano-concave
convexo-concave
These lenses diverge light from a virtual focus.
The focal length of a lens is generally NOT
half-way between the center of curvature
and the vertex of the lens, but it depends
on the lens material’s index of refraction
and on the shape of the lens.

12. Ray Diagrams 1/f = 1/do + 1/di di/do = si/so.
Converging and Diverging Lenses
1. Rays passing through the optical center pass
straight through without refraction.
2. Incident rays parallel to the principal axis
refract through the focus or diverge away
from the focus.
3. Rays passing through or toward the focus
refract parallel to the principal axis.
Just like mirrors,
1/f = 1/do + 1/di
and
di/do = si/so.

13. Click here, here, and here to view simulations showing image formation
in converging and diverging lenses
using these three important rays.

14. The PhET simulation linked here
shows image formation in a converging lens.
Learn more about image characteristics here.
Images formed by converging lenses may be:
1. real, virtual, or non-existent
2. upright or inverted
3. reduced, enlarged, or same size
4. in front or behind the lens

15. The image characteristics depend on the object’s position with respect
to one and two focal lengths
(1f and 2f) away from the lens. 2f f

16. object is beyond two focal lengths:
image is real, inverted, and reduced
object is exactly twice the focal length:
image is real, inverted, and the same size
object between one and two focal lengths:
image is real, inverted, and enlarged
object is on the focus:
no image; rays reflect parallel
object is inside the focus:
image is virtual, upright, and enlarged

17. The simulation linked to the optics applets
here shows image formation in all
types of lenses and curved mirrors.
Learn more about image characteristics here.
Images formed by diverging lenses are always:
1. virtual
2. upright
3. reduced
4. located in front of the lens between the
focus and the lens

18. General Image Trends real images are always inverted
virtual images are always upright
real images are always behind the lens
virtual images are always in front
of the lens
negative image distance means
virtual image
positive image distance means real image
real images may be projected onto a screen; virtual images may not