Image Formation and the Lens: Object Beyond The Focal Point




A convex lens is shown below with its focal points displayed (the dots). An object is
located to the left of and at a distance of 2f to the lens. A dotted line has been drawn
normal to the middle of the lens surface as a guide (the guide line).

Ray 1

From the tip of the arrow (top) draw a line parallel to the guide line until you
reach the midpoint of the lens

Draw a line from the ending position of your previous line through the right
focal point, letting it extend some distance beyond the focal point

Ray 2

Draw a line from the arrow tip through the left focal point to the midpoint of
the lens.

Draw a line from the ending position of your previous line parallel to the
guide line. Extend this line beyond the point where it intersects the ray 1.

Ray 3

Draw a line from the arrow tip through the exact midpoint of the lens.
Extend this line slightly beyond the point where it intersects ray 1.
The intersection of the three lines in your drawing above represent the position of the
real image formed by the tip of the arrow. How does the height of your image
compare with that of the object? Is your object upright or inverted?
Show that the ‘thin-lens equation’ predicts the position of the image. Use a ruler to
measure the variables (o, i, and f)
i
The magnification of a lens is defined as m   . Determine the magnification from
o
your measured variables.
PHYS 1112
Ray Tracing Worksheet
1
Image Formation and the Lens : Object Beyond The Focal Point

Draw three rays for the arrangement below, where the object is more than 2f from the
midpoint of the lens. Note, the focal length has changed!



The intersection of the three lines in your drawing above represent the position of
the image formed by the tip of the arrow. Does the object show an enlargement
or reduction in the image height compared to the actual object height? Is your
object upright or inverted?
Show that the ‘thin-lens equation’ predicts the position of the image. Use a ruler
to measure the variables (o, i, and f)
i
The magnification of a lens is defined as m   . Determine the magnification
o
from your measured variables.
PHYS 1112
Ray Tracing Worksheet
2
Image Formation and the Lens : Object Between F and Lens




An object at the focal point

A convergence lens is shown below with its focal points displayed (the dots). An
object is located to the left of and at a distance of 1/2f to the lens. A dotted line
has been drawn normal to the middle of the lens surface as a guide (the guide
line).
Ray 1

From the tip of the arrow (top) draw a line parallel to the guide line until you
reach the midpoint of the lens

Draw a line from the ending position of your previous line through the right focal
point, letting it extend some distance beyond the focal point
Ray 2

Starting with ray 1 as it extends from the midpoint of the lens to the focal point,
use a dashed line to extend this ray 1 beyond the other focal point (to the left in
this case).
Ray 3

Draw a line from the arrow tip through the exact midpoint of the lens. Note that
the geometry of the situation makes it impossible to have this ray intersect ray 1,
as before. Instead, use a dashed line to extend this line back toward the left
focal point until it intersects ray 1.

Is the intersection of ray 2 and ray 3 a real or virtual image? What is the difference?

Calculate the magnification for this system using measured variables.
PHYS 1112
Ray Tracing Worksheet
3
Image Formation and the Lens: Concave Lenses



A concave lens is shown below with its focal points displayed (the dots). An object is
located to the left of and at a distance of 2f to the lens. A dotted line has been drawn
normal to the middle of the lens surface as a guide (the guide line).

Ray 1

From the tip of the arrow (top) draw a line parallel to the guide line until you
reach the midpoint of the lens

Draw a line from the left focal point through the end of ray 1 at the midpoint
of the lens using a dashed line. Continue this line beyond the lens with a
solid line.
Ray 2

Draw a line from the arrow tip through the exact midpoint of the lens. Extend
this line slightly beyond the lens.
The intersection of the two lines in your drawing above represent the position of the
image formed by the tip of the arrow.

Is this a real or virtual image? How do you know?

Is the image inverted or upright?

Has the image been enlarged or reduced?


Test to see if the ‘thin-lens equation’ works for a concave lens by using measured
variables from your diagram above. Does it?
Test the magnification equation using your measured variables. Does this
equation work for a concave lens?
PHYS 1112
Ray Tracing Worksheet
4
Image Formation and the Lens: Concave Lenses II





A concave lens is shown below with its focal points displayed (the dots). An object is
located to the right of the focal point of the lens. A dotted line has been drawn
normal to the middle of the lens surface as a guide (the guide line).

Ray 1

From the tip of the arrow (top) draw a line parallel to the guide line until you
reach the midpoint of the lens

Draw a line from the left focal point through the end of ray 1 at the midpoint
of the lens using a dashed line. Continue this line beyond the lens with a
solid line.
Ray 2

Draw a line from the arrow tip through the exact midpoint of the lens. Extend
this line slightly beyond the lens.
The intersection of the dashed line of ray 1 and ray 2 represents the formation of the
image of the tip of the arrow. Draw in your arrow.

Does it appear upright or inverted?

Has the arrow been enlarged or reduced?

Is this image real or virtual?
Use the thin-lens equation to show that the image position can be predicted by
knowing the object position and the focal length (measure these variables using a
ruler to the nearest millimeter).
Calculate the magnification of the image from your measured variables. Compare this
to the actual height of your object and image (measure this directly).
PHYS 1112
Ray Tracing Worksheet
5
Image Formation and the Spherical Mirror I


An light source has been placed in front of the spherical mirror below, with radius of
curvature.

Measure the radius of curvature and calculate the focal length of this mirror.
Place a dot at the focal point for reference.
Three collimated rays of light are displayed exiting the light source.

Continue each displayed ray until it reaches the surface of the mirror.

From the point of contact of a ray and the mirror, continue each ray by drawing a
straight line through the focal point.
C



An object (the arrow) has been placed in front of the spherical mirror below, with
radius of curvature and focal point shown.
Ray 1

Draw a line from the arrowhead to the center of the mirror. This ray reflects as if
it is incident on a planar mirror. Draw the reflected ray
Ray 2

Draw a line from the arrowhead through the focal point until it reaches the
surface of the mirror. The reflected ray will be parallel to the guide line. Draw
the reflected ray until it intersects ray 1.
C


F
Draw your arrow. Does it appear upright or vertical?
Is this image an enlargement or reduction of the object?
PHYS 1112
Ray Tracing Worksheet
6
Image Formation and the Spherical Mirror II


Below is a spherical mirror with the focal point indicated. A guide line has been drawn
for reference. An object (the arrow) has been placed nearby.
Measure the focal point. From this value, calculate the radius of curvature and place a
dot at that location on the guideline.
C = _____________





Ray 1

Draw a line from the focal point to the tip of the arrow.

Where this ray crosses the surface of the mirror nearest the object, draw a
dashed line parallel to the guideline back toward the focal point.
Ray 2

Draw a line parallel to the guideline from the tip of the arrow to the surface of the
mirror.

From the point of contact with the mirror, draw a dotted line to the focal point.
Ray 3

Draw a dotted line from the center of curvature to the surface of the mirror such
that, if extended, it would connect to the tip of the arrow.
The intersection of the dashed line of these three rays represents the formation of the
image of the tip of the arrow. Draw in your arrow.

Does it appear upright or inverted?

Has the arrow been enlarged or reduced?

Is this image real or virtual?
Measure the object height and image height. Calculate the magnification.
F
PHYS 1112
Ray Tracing Worksheet
7