PHYSICS 545
R. J. Wilkes
1st Week Lab: Elementary Lens/Mirror Optics Experiments
Tuesday night: items 1 and 2 below, Thursday night: 3 and 4.
Apparatus required:
Pasco Optical Bench kit, assorted positive and negative thin lenses (one positive meniscus),
pinhole screen, plane mirror, diffusing glass, red and blue color filters. See figures at end of this
document for setups referred to in text.
1. Test for sign of lens
Take a sample lens, hold it near your eye, and sight on a distant object (e.g., a table). Move the
lens up and down slightly. If the lens is converging (positive), the object appears to move in the
opposite direction; if the apparent motion is in the same direction, the lens is diverging
(negative). If there is no motion, the lens has zero power. The latter effect can be used to find the
focal length of an unknown lens, by placing it in contact with lenses of known focal length and
opposite sign. Try placing the +150mm and -150mm lenses together to check this.
2. Measuring focal lengths
a) by casting an image of a distant object. Line up the 150mm positive (convex) lens and a piece
of paper with a ceiling lamp and move the lens back and forth until you get an image of the lamp
projected onto the paper. If the distance to the object is much greater than the distance from lens
to paper, the latter distance is a good approximation to the focal length of the lens. Try this first
with the 150mm lens and then with an "unknown" (ie, unlabelled) lens. This method only works
for positive lenses.
b) by measuring object-image distances. Set up the optical bench with the crossed-arrow target
on the lamp window. Put the arrow target at the 100mm mark and the viewing screen at 700mm.
Interpose the 75mm positive (convex) lens and move it around until a sharp image of the pinhole
is obtained on the screen (figure 1). Note the object and image distances and find f' from the
Gauss Equation
1/f ' = 1/l ' - 1/l
(where we use the standard "professional" sign convention, in which displacements are positive
when they go from left to right; l is negative if the object is to the left of the lens). Repeat for the
150mm lens. Note that there are 2 image locations for each lens, symmetrically located, and
compare their magnifications. This method only works for positive lenses, and requires the
measurement of two lengths.
1
Next, use blue and red color filters to observe the wavelength dependence of the focal length.
The arrow will be too hard to see when using color filters, so instead use the filament of the lamp
as the object. The difference in focal length is small but measurable.
c) by autocollimation. This procedure makes use of the fact that diverging rays from a point
object located at f' will be parallel after passing through a lens, and vice versa. Thus a mirror
located (anywhere) behind a positive lens will reflect the parallel rays back into the lens and
form an image at the object location (or right next to it, if the mirror is tilted a tiny bit) if the
object is at f'. Use a pinhole as the object, replace the screen with a plane mirror, and use the
setup shown in figure 2a to find the focal length of a convex lens. Move the lens around until a
sharp image of the pinhole appears on the pinhole plane. Make sure you are not looking at
reflection from back surface of the lens - the image should move when you wiggle the plane
mirror, not the lens.
Next use the 75mm convex lens in the setup shown in figure 2b to measure the focal length of a
negative (concave) lens. First, repeat the setup in fig. 1, and measure the lens-to-image distance
for the +75mm lens. Next, put the mirror in front of this image position. The negative lens can
just be attached to the same mount as the mirror. Now move the positive lens around until you
get a sharp image of the pinhole reflected on the pinhole screen. Then you know that the negative
lens is making rays from the pinhole arrive at the mirror parallel to the axis, so the (unsigned)
focal length of the negative lens plus the distance between the positive and negative lenses is
equal to the image distance for the positive lens alone (as measured, or just calculated using the
Gauss equation, given the object distance and the focal length): | fneg | + d = l’pos
3. Simple optical instruments.
Try making the following (figures 4a-c) as time permits. You can remove the lamp and screen
from the optical bench, or just hold the lenses in your hands. All of these have the same basic
operating principle: the objective lens casts an image of the object at the focus of the ocular
(eyepiece).
a) Astronomical (simple refractor) telescope. Try this with the 18mm and 150 mm convex
lenses. What is the magnification in terms of f1 and f2? Also try making a Newtonian (reflecting)
telescope using the 50mm concave mirror (tilted slightly) and the 18mm convex lens.
b) Galilean (non-inverting) telescope. Here, the positive objective lens image becomes a virtual
object for the ocular.
c) Compound Microscope.
4. Determination of refractive index and radii of curvature.
Figure 3a shows the autocollimation method for finding the radius of curvature of a spherical
mirror. A pinhole at the center of curvature of the mirror will be imaged on the pinhole plane.
The Lensmaker's Equation shows that if the radii of curvature and focal length of a lens are
known, the refractive index may be calculated: 1/f' = (n-1){(1/r1) -(1/r2)}
2
Suppose rays from a point source P arrive at normal incidence on the second surface of a doubleconvex lens of known focal length (Fig. 3b). The rays emerge without refraction and form a
virtual image at P', which is the center of curvature of surface 2. Thus (for a thin lens) we have
l'=r2 and 1/r2 - 1/l = 1/f'
(note that both r2 and l are negative using our sign convention). Some light is reflected internally
at surface 2, so it behaves like a spherical mirror; the reflected light retraces the solid-line path,
so that a faint image will be seen coincident with the pinhole when l is just such that the rays are
normally incident. For a positive lens of known f', measure l and find r2 from the above equation.
This procedure can be combined with autocollimation, to find f', ri and n in one fell swoop, at
least for positive meniscus (convex-concave) lenses. Take an unknown meniscus lens, make sure
it is positive via procedure (1) above, and set up as in figure 3c, with the plane mirror on the
convex side of the lens. As you move the lens about between the pinhole and the mirror, you will
observe three distances P which give sharp images on the pinhole screen, corresponding to
reflections from the plane mirror (ie, for the lens as a whole) and the two surfaces of the lens.
The plane mirror image is easy to identify; it moves when you wiggle the mirror. The front lens
surface (surface 1) acts as a simple spherical mirror, and the back surface makes the third image
as in Fig. 3b. Watch carefully, the back surface and whole-lens images are close together. How
would you apply the equations above to find f', r1, r2 and n?
3
4
5