Transcript light ray

Upcoming Schedule
Dec. 1
22, 23.1,
23.4, 23.5
Dec. 3
boardwork
Dec. 5
23.6-23.9
Quiz 10a
Dec. 8
boardwork
Dec. 10
23.2-23.3
Quiz 10b
Dec. 12
review
Dec. 15
Final Exam
4-6 pm
“You do not really understand something unless you can explain it to your
grandmother.”—A. Einstein
Chapter 23
Geometric Optics
23.1 The Ray Model of Light
Although light is actually an electromagnetic wave, it generally
travels in straight lines.
We can describe many properties of light by assuming that it
travels in straight-line paths in the form of rays.
A ray is a straight line along which light is propagated. In
other contexts, the definition of ray might be extended to
include bent or curved lines.
A light ray is an infinitely thin beam of light. Of course, there
really isn’t such a thing, but the concept helps us visualize
properties of light.
Light rays from some
external source strike an
object and reflect off it in all
directions.
We only see those light rays
that reflect in the direction
of our eyes.
If you can see something, it
must be reflecting light!
Zillions of rays are simultaneously reflected in all directions
from any point of an object. We won’t try do draw them all!
Just enough representative ones to understand what the light
is doing.
We will skip sections 23.2 and 23.3 for now, and come back to
them later. This was originally done to match the lab schedule,
and seemed to work well.
23.4 Index of Refraction
Light travels in a straight line except when it is reflected or
when it moves from one medium to another.
Refraction—the bending of light when it moves from one
medium to a different one—takes place because light travels
with different speeds in different media.
The speed of light in a vacuum is c = 3x108 m/s. The index of
refraction of a material is defined by
c
OSE :
n =
,
v
where c is the speed of light in a vacuum and v is the speed of
light in the material.
Because light never travels faster than c, n  1. Table 23-1
lists several values of n. For water, n = 1.33 and for glass, n
1.5.
Example 23-7 Calculate the speed of light in diamond (n =
2.42).
c
n =
v
c
v =
n
3×108 m/s
v =
2.42
v = 1.24×108 m/s
23.5 Refraction: Snell’s Law
When light moves from one medium into another, some is
reflected at the boundary, and some is transmitted.
The transmitted light is refracted (bent).
Figure 23.18 shows refraction. The angle 1 is called the angle
of incidence, and the angle 2 is called the angle of refraction.
Light passing from
air (n  1) into water
(n  1.33).
Light bends towards
the normal to the
surface because it
slows down in water.
http://www.phy.ntnu.edu.tw/java/light/flashLight.html
Light passing from
water (n  1.33) into
air (n  1).
Light bends away
from the normal to
the surface because
it speeds up in air.
Read about optical illusions in section 23.5.
Snell’s law, also called the law of refraction, gives the
relationship between angles and indices of refraction:
OSE:
n1 sin  θ1  = n2 sin θ2  .
air (n1)
air (n1)
1
1
2
water (n2)
2
water (n2)
 is the angle the ray makes with the normal!
Demo: coin-in-the-bowl.
Example 23-9 Calculate the apparent depth of an object one
meter below the surface of water. (Angles have been
exaggerated for ease of viewing).
n1
Light reflected off the coin actually
follows the solid yellow path.
x
1
Your brain “thinks” light travels in a
straight line path, and imagines the
light followed the dotted line path.
H
D
n2
2
The coin appears to be a distance H
beneath the surface of the water.
n1 sin  θ1  = n2 sin θ2 
OSE:
sin  θ1  = n2 sin  θ2 
θ1 = n2 θ2
(valid for small* angles)
*15° or less
n1
from the drawing:
x
x
tan  θ1  =
tan  θ2  =
H
D
x
1
H tan  θ1  = x = D tan θ2 
H
H θ1 = D θ2
D
n2
(nair = 1)
2
(small* angles)
θ1 = n2 θ2  H n2 θ2 = D θ2
D 1m
H= =
= 0.75 m
n2 1.33