Physics 1809: Optics 1 - Activities with Light Rays
Purpose of this Minilab
• Apply the basics of ray tracing to learn about
reflection and refraction of light.
Physics 1809: Optics 1 - Activities with Light Rays
Activity 1: Light Reflection at Plane Surfaces
Angle of incidence
Angle of reflection
i
r
ni
Index of refraction
of the two materials
nt
t
Angle of
transmission
(refraction)
Physics 1809: Optics 1 - Activities with Light Rays
…..the laws….
Law of Reflection: r  i
Snell’s Law of Refraction:
ni sin i  nt sin t
Incident, reflected, and transmitted ray lie in one plane.
Verify the law of reflection using a plane mirror.
Verify your homework result on a 90 plane mirror.
Physics 1809: Optics 1 - Activities with Light Rays
Checking the law of reflection with a plane mirror
r
45
0
Polar graph
paper
90
i
Light Source
45
135
90
180
135
Mirror
Physics 1809: Optics 1 - Activities with Light Rays
Measuring refraction
Polar graph
paper
45
0
90
Use Snell’s
law to
determine
nplastic.
i
Light Source
45
135
Light must
hit the center
of the flat side
t
90
180
135
Semicircular
lens nplastic
Physics 1809: Optics 1 - Activities with Light Rays
Measuring angle of total internal reflection
Polar graph
paper
45
0
90
45
135
Light must
hit the center
of the flat side
crit
90
180
135
Semicircular
lens
Light Source
Physics 1809: Optics 1 - Activities with Light Rays
Snell’s Law for Critical Angle
=1
n plastic sin critical  nair sin 90
1
n plastic 
sin  critical
Physics 1809: Optics 1 - Activities with Light Rays
Light beam displacement by plane parallel plate
Light Source

’
t
d
Physics 1809: Optics 1 - Activities with Light Rays
Light beam displacement by plane parallel plate
Polar graph
paper
Light
Source

’
Let the beam hit the
rectangle in center
of the polar paper
t
• Trace light ray on polar graph paper.
• Outline location of rectangular plastic on paper.
• Measure angles  and ’.
• Measure widths d and t.
d
Physics 1809: Optics 1 - Activities with Light Rays
Light beam displacement by plane parallel plate

cos  
d  t sin  1 
'
n
cos



• Use one incident angle  (and corresponding ‘ and d and t)
 calculate n.
• Use this calculated n to predict the displacement d for a different incident
angle.
(Hint: You will also need to use Snell’s Law for this calculation.)
• Verify experimentally d for the new angle.
Physics 1809: Optics 1 - Activities with Light Rays
Activity 2: Reflection and Refraction at Spherical Surfaces
Getting the radius R of a concave mirror
Concave mirror, reflecting side here.
1
D2 

R   x 
2
4x 
R
x
D
Physics 1809: Optics 1 - Activities with Light Rays
Alternative method to get R …..
Polar graph
paper
Move mirror until
curvature matches
the curvature on
polar graph paper.
then measure R
as shown.
R
Physics 1809: Optics 1 - Activities with Light Rays
Finding the focal point of the concave mirror
Regular graph paper: Trace the rays and determine f.
Light
Source
parallel rays
f
Physics 1809: Optics 1 - Activities with Light Rays
Finding the focal point of the convex mirror
Regular graph paper: Trace the rays and determine f. Extend the light rays
backward to where they
seem to come from.
Light
Source
Virtual image
(isn’t really
there).
parallel rays
f
Physics 1809: Optics 1 - Activities with Light Rays
Imaging with the convex mirror
Regular graph paper: Trace the rays and determine f.
Here is our
object point
Light
Source
Semicircular lens
S
P
Physics 1809: Optics 1 - Activities with Light Rays
Thin Lens Equation (how to calculate focal length from the
radii of a lens and it’s index of refraction)
1 1 
1
 n  1   
f
 R1 R2 
Each lens has two interface with the air (#1 and #2).
Interface #1 is the one that is encountered by the light when entering the lens
Interface #2 is the one that is encountered by the light when exiting the lens.
Interface #1 has
radius R1.
Interface #2 has
radius R2.
Physics 1809: Optics 1 - Activities with Light Rays
Thin Lens Equation (how to calculate focal length from the
radii of a lens and it’s index of refraction)
1 1 
1
 n  1   
f
 R1 R2 
Sign rules for R1:
R1 positive
R1 negative
R2 positive
R2 negative
Physics 1809: Optics 1 - Activities with Light Rays
Example of using the lens equation
A double concave lens (concave on interface #1 and also on #2)
with both radii being 5cm and the index of refraction n=1.65 :
 R1 = - 5 cm and R2 = + 5 cm


1 1 
1
1 
(2)
1.25
 1
 n  1     1.65  1


0
.
65



f
R
R

5
cm
5
cm
5cm
5cm


2 
 1
f   4 cm
Physics 1809: Optics 1 - Activities with Light Rays
The Imaging Equation for Lenses and
Mirrors
1
1
1


S
P
f
S: Object Distance
P: Image Distance
f: Focal Length
For Mirrors:
R
f 
2
where R = Radius of Mirror
1
1
2


S
P
R
Physics 1809: Optics 1 - Activities with Light Rays
Sign Rules For Lenses and Mirrors
f
Convex Lens:
Concave Lens:
Convex Mirror:
Concave Mirror:
+
+
Means: a positive number
Most objects are real.
Real objects:
Virtual objects:
S is positive
S is negative
Real images:
Virtual images:
P is positive
P is negative
Physics 1809: Optics 1 - Activities with Light Rays
Example of signs for f, S, and P
Convex mirror:
f is negative
Real object
Virtual image
Light
Source
S
positive
P
negative
Physics 1809: Optics 1 - Activities with Light Rays
Using the Desk Lamp
Lamp Plug (black) must be plugged
into dimmer plug.
Dimmer plug (white) must be plugged
into power outlet.
Dimmer
On/Off
switch
of lamp