IB PHYSICS HL2
OPTICS LAB: LENSES AND MIRRORS
Purpose
In this lab we will observe the images formed by lenses and mirrors and use the thin lens
equation to calculate their focal lengths. We will also set up a slide projector, an overhead
projector, and make some general observations about how these instruments form images.
Background
Thin, spherical lenses and mirrors can both be used to form images. This is because they have
the ability to bring light rays from distant objects to a focus (see diagrams below).
Light rays from an object an infinite distance away will be parallel. When parallel rays pass
through a lens, they will be refracted to a single point on the other side of the lens. This point is
called the focal point, and the distance between the center of the lens and the focal point is called
the focal length f of the lens.
Focal
point
Object at
infinity
Converging lens
Parallel rays striking a mirror will be reflected to a point: the focal point of the mirror. The
distance from the mirror to the focal point is the focal length of the mirror. It is found that for
rays not too far from the mirror’s optical axis (axis of symmetry) the focal length is one-half its
radius of curvature: f = R/2.
Focal
point
Object at
infinity
Converging mirror
Light rays from nearby objects will not be parallel. They will be refracted or reflected in such a
way as to form an image near the focal point. Where the image forms depends on the focal
length of the lens or mirror and on how far away the object is. To calculate the image location,
we can use the thin lens equation.
The Thin Lens Equation
Both lenses and mirrors obey the thin lens equation:
1 = 1 + 1
f
di
do
(1)
where



f is the focal length;
do is the object distance: the distance from the object emitting the light to the center
of the lens or mirror;
di is the image distance: the distance from the lens or mirror to the image formed.
For converging lenses and mirrors, f is a positive number. Converging lenses and mirrors cause
light rays to converge to a point, as in the two diagrams above.
For diverging lenses or mirrors, f is considered negative. Diverging lenses and mirrors cause
light rays to diverge. The focal point is the point from which the rays appear to diverge. See
diagrams below.
Focal point
Diverging Lens
Focal
point
Diverging Mirror
The image distance, di, can be positive or negative depending on where the image forms.
Consider first a converging lens (refer to the first diagram above). When the object is located
outside its focal length, the converging lens will form an image beyond the focal point on the
other side of the lens. This is called a real image, since it occupies a real position in space. (For
instance, the image can be observed on a screen placed at the image distance.) In this case the
image distance is considered positive.
In the limiting case where the object is located at infinity (or far enough away to be considered at
infinity), the image forms at the focal point. That is,
f = di (object at infinity)
as is evident from the thin lens equation, with do very large.
As the object moves closer to the lens, the image moves farther away on the other side, as is also
evident from the thin lens equation. When the object moves inside the focal length of the lens,
the image will form on the same side of the lens as the object. The image distance is considered
a negative number, and the image is called a virtual image.
A virtual image is one that can be seen only by looking through the lens. It cannot be projected
on a screen and its position cannot be directly measured. Instead, we must measure the image
distance by an indirect method (see the method of parallax, below).
Converging mirrors also form real and virtual images. The image will be real and di is a positive
number when the object is located outside the focal length of the mirror. The image will form on
the same side of the mirror as the object, outside its focal point. An object at infinity will form a
real image at the focal point.
When the object moves inside the focal distance of the mirror, the image becomes virtual – we
have to look into the mirror to see it – and it appears to form on the other side of the mirror from
the object. In this case, the image distance di is considered to be a negative number.
Diverging lenses and mirrors form virtual images only - the images they form cannot be
projected on a screen. For a diverging lens the image forms on the same side of the lens as the
object. For a diverging mirror, the image forms on the opposite side of the mirror from the
object. For both, the image distance i is taken to be a negative number, as is the focal length f.
Magnification
The magnification of an image can be calculated in two ways:
(2)
m = -hi/ho
or
(3)
m = d i /d o
where m is the magnification, ho is the height of the object and hi is the height of the image, and
di and do are the image and object distances, respectively.
In Part A, you will investigate the images formed by lenses and mirrors. For each of the
images you find, record the positions of the object, lens, and screen in your lab
notebook. Later, you will calculate the object distances, image distances, and focal
lengths for each image. Also record the heights of the object and of the image (omit for
object at infinity) and describe the image as real or virtual, enlarged or reduced, upright
or inverted.
In Part B, you will set up three simple optical instruments: a microscope, an overhead
projector, and a slide projector.
For reference:
Thin Lens equation
1 = 1 + 1
f
di
do
Magnification
m = hi/ho= di/do
Equipment








Optics bench
Object lamp
Screen
Converging (convex) lens
Converging (concave) mirror
Table lamp
Object for optical bench
Light source at “infinity”
f = focal length
di = image distance
do = object distance
M = magnification
hi = height of image
ho = height of object
di = dist. from lens to image
do = dist. from lens to object
Part A. Investigate image formation by a convex lens and a concave mirror.
 Convex Lens 1
1. Object at infinity. Place the longer focal length lens on the optics bench and
point it out the window or door and find an image of a distant object. In this case,
the focal length is the same as the image distance. Determine and record this.
2. Nearby objects. Place the object lamp at one end and the screen at the other
end of the optics bench. Put the lens in between.
First, get a qualitative overview of the object/image relationship. Observe and
describe how the image and its position change for different object distances.
Then measure the positions and the heights of the object and image for object
placed at approximately 3f, 2.5f, 2f, 1.5f and .5f, where f is the focal length as
determined above.
For the last object position (object inside focal length) a qualitative description is
sufficient, since no real image exists.
 Convex Lens 2
-Repeat the procedure above for the convex lens of shorter focal length.
 Concave Mirror
1. Object at infinity. Place the mirror on the optics bench and point it out the
window or door and find an image of a distant object. In this case, the focal
length is the same as the image distance. Determine and record this.
2. Nearby objects. Place the object lamp at one end of the bench and the mirror
at the other end.
First, get a qualitative overview of the object/image relationship. Observe and
describe how the image and its position change for different object distances.
Then measure the positions and the heights of the object and image for object
placed at approximately 3f, 2.5f, 2f, 1.5f and .5f.
For the last object position (object inside focal length) a qualitative description is
sufficient, since no real image exists.
Part B. Optical Instruments
For each of the following, describe the image (real or virtual/upright or inverted),
estimate the image magnification, and record the length of the instrument (the
distance between the lenses).
Overhead Projector
Examine this device for a few minutes. How does this device make use of lenses
and mirrors to produce the desired effect (For example, why isn’t the teacher’s
writing reversed left to right)? Describe in words and include a diagram. Note
the number of lenses, number of mirrors, and the location of each.
Slide Projector
How does this instrument work? Why is it sometimes confusing when placing
slides into a projector? What “case” (choose from #1-6) for a converging lens is
this instrument?
*This is a discussion only…you will not actually experiment with this!
Compound Microscope
How many lenses are used in a compound microscope? What type of image (real
or virtual?) does each lens form? Why is it sometimes confusing to adjust a slide
in a microscope?
Analysis:
A. Lenses and Mirrors. Calculate the focal lengths and magnifications for each
image, for each lens or mirror. Take an average for the focal lengths and compare
to the value obtained for the lens or mirror with the sun (“infinite distance” away).
Compare the magnifications as determined by measurement (M=hi/ho) to that
given by theory (M=-di/do). Discuss the sources of error for ach of these
measurements.
B. Optical Instruments. Include your answers to the questions posed above for
each optical instrument and your diagrams for the light rays in each type of
optical instrument. The diagrams should show the light rays from the time they
leave the object until they form the image.
C. For each of the following, draw ray diagrams to scale in your lab book:
*Use rulers and compasses for these!
(1) convex lens with object outside the focal point (do >f)
(2) convex lens with object inside the focal point (do < f)
(3) concave lens with object outside the focal point (do >f)
(4) concave mirror with object outside the focal point (do > f)