Physics 102
Ray Tracing
Juan Guerrero, Phuc La
April 16, 2006
Abstract
The purpose of this lab is to verify the reflective properties of a plane mirror and
locate the focal point of a convex mirror. The lab is also to find the radius of
curvature of a concave mirror and the index of refraction of a double convex lens.
Finally, it is to find the focal point for a concave lens and the critical angle for total
internal reflection in a plano-convex lens.
Data
Flat mirror
The angle of incidence
oC
20.05
The angle of reflection
oC
20.06
Convex and Concave mirrors
Focal point of convex mirror
cm
2.80
Focal point of concave mirror
cm
2.60
Convex and Concave lens
Focal point of convex lens
cm
11.70
Focal point of concave lens
cm
11.70
The plano-convex lens
The critical angle is 44.50o.
Graphs
Diagrams are in attached papers.
Calculations
Flat mirror
In the flat mirror, the angle of incidence is equil to the angle of reflection. In the
experiment, the angle of incidence is 20.05o. The angle of reflection is 20.06o and
closes to the angle of reflection. So, the angle of incidence should be the same
as the angle of reflection.
The difference error is
% diff 
| 20.06  20.05 |
100 %  0.05 % Should be in the percent error
20.06  20.05
2
section
Convex mirror
The distance from the focal point to the mirror is 2.80 cm. The radius is two times
the focal length.
R = 2f = 2 * 2.80 cm = 5.60 cm
The image is behind the mirror.
Concave mirror
The distance from the focal point to the mirror is 2.60 cm. The radius is two times
the focal length.
R = 2f = 2 * 2.60 cm = 5.20 cm
The diameter of the concave mirror is
D = 2R = 2 * 5.20 cm = 10.4 cm
The image is in front of the mirror.
Convex lens
Several tangent lines are drawn to the lens. A perpendicular line from the tangent
point is drawn back toward the center of curvature. The distance from the tangent
point to where perpendiculars cross is R. R is 10.70 cm. The convex lens has the
same curvature so
Ri = Rr = R = 10.70 cm
Also, the focal length is 11.70 cm
using the lensmakers’ equation, the index of refraction is
1
1
1
1 1
2
 (n  1)(  )  (n  1)(  )  (n  1)( )
f
Ri Rr
R R
R
n
10.70 cm
R
 1
 1 1.457
2f
2 *11.80 cm
Diverging lens
Using the diagram for the diverging lens, the focal point of the double concave
lens is 11.70 cm
Plano-convex lens
The critical angle is the angle between the incidence ray and the normal line of
new flat trace. The critical angle is 44.50o.
Results
Flat mirror
The angle of incidence
oC
20.05
The angle of reflection
oC
20.06
Convex mirror
Focal point of convex mirror
cm
2.80
Concave mirror
Focal point of concave mirror
cm
2.60
Convex lens
Focal point of convex lens
cm
11.70
Radius
cm
5.60
Radius
cm
5.20
Radius
cm
10.70
Diameter
cm
10.4
The index of refraction (n)
1.457
Concave lens
Focal point of convex lens
cm
11.70
Plano-convex lens
The critical angle
oC
44.50
% Error
In the experimentt, the flat mirror has two values to calculate the different error.
The angle of incidence
oC
20.05
The angle of reflection
oC
20.06
% diff
%
0.05
Questions
1. Common uses for concave mirrors are in telescopes that uses mirrors to
magnify an image onto an eyepiece and satellite dish which is concave
mirror to reflect microwave waves onto an antenna.
Common uses for convex mirrors are sometimes used for home
decorating, a security mirror in a shop and a wide angle mirror on a bus.
2. A convex lens is used to obtain a real image of an object like diagram 1.
The concave lens is put in place like diagram 2.
The real image in diagram 1 becomes virtual object in diagram 2. Concave lens
uses the virtual object to form a real image. So, the effects of a convex lens can
be negated by a concave lens.
3. Below picture is an illustration.
The air above the water haves index of refraction n2 and the water has an index
of refraction n1. Besides, n2 equals 1 and n1 equals 1.33. θ angle is
sin  
n2
1

 0.752
n1 1.33
   48.8
θ is critical angle and equals 48.8o. The person can see the object that is out of
the water if the person looks toward the surface at an angle less than the critical
angle. At 48.8o, the person can see the object on the surface of the water. At
angles greater than the critical angle, the person sees a reflection of the part of
the object in the water.
Conclusion
In flat mirrors, the angle of reflection equals the angle of incidence. Incomimg
parallel rays focus to a point on concave mirror and gives real image. The light is
reflected from the outer and the reflected light is from the point behind the convex
mirror. Diverging lenses always give upright virtual image. In converging lens,
when object distance is less than focal length, the image is an upright virtual
image. When the object’s distance is greater than the focal length, the image is
an inverted real image. In plano-convex lens, the light escapes from the flat side
of the lens when the angle is less than the critical angle. The light failed to
escape from the flat side of the lens when its angle is greater than the critical
angle.
98/100