Download Physics 425L Optics Laboratory Chromatic Aberration

Physics 425L
Optics Laboratory
Chromatic Aberration
Introduction
In this lab you will study chromatic aberration of lenses and how to minimize it.
The index of refraction of a material, n, is a function of the wavelength of light, n=n(λ).
1
1
1
From the lens maker’s equation:
= (n l −1)( − ) and knowing that n=n(λ), one
f
R1 R2
concludes that the focal length, f, of a simple lens is a function of wavelength, f=f(λ).
1 1 1
Since,
+ = the image distance will also be a function of wavelength, resulting in a
so si f
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blurred image if more than one wavelength is present. This is called chromatic
aberration. Newton mistakenly thought there was no way eliminating chromatic
aberration, which is what motivated him to develop the reflecting (Newtonian) telescope.
€ Cauchy fit n(λ) with the following empirical formula:
B C
(1)
n( λ) = A + 2 + 4
λ λ
Often, the first two terms are sufficient, thus knowing the index of refraction at 2
wavelengths is sufficient to obtain n(λ).
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Experiment
For the first experiment you will observe chromatic aberration qualitatively. Place lens
8, its focal length away from the point light source to insure a parallel beam of light (see
figure). Observe the beam of light on the wall. What do you see? Report this in your lab
notebook.
Department of Physics
Jan. 12 2009
University of Missouri-Kansas City
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Replace lens 8 with lens 5, again insure that a parallel beam of light leaves the lens.
What do you observe? Lens 5 is an achromat, it’s made of 2 different types of glass,
specifically tailored to reduce chromatic aberration.
Place the optical mask after lens 5, followed by lens 1. Insure that lens 1 is well
centered with respect to the central beam from the optical mask and place it along the
optical rail so that it is directly over a whole number (distance from the beginning of the
rail).
Allow light to pass through the set of 3 holes that are on the smallest bolt circle of the
optical mask. These rays of light are sufficiently close to the optical axis that we can
ignore spherical aberration. Now place the blue interference filter (see figure) after the
optical mask.
Department of Physics
Jan. 12 2009
University of Missouri-Kansas City
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Place the camera on the last mount and move the mount so that the three rays from the
optical mask come into focus. Now move the mount so that it is directly over the first
whole number to the left of the focus, set up the dial indicator (see figure) and zero it.
Note that the camera sensor is 2.83 cm closer to the lens than this number.
When all of the components are in place the optical system should look like this.
Department of Physics
Jan. 12 2009
University of Missouri-Kansas City
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Now move the camera so that the 3 rays of blue light come into focus. From the
readings of the dial indicator (The dial indicator reads in inches.) and from the rail you
will be able to precisely determine the focal length of the lens for blue light. Replace the
blue interference filter with the yellow one, and repeat your measurements. To insure
accurate measurements, you should not move the dial indicator.
Repeat this
measurement with the red filter.
Repeat these measurements with lens 6 and also lens 3.
One common method for reducing chromatic aberration is to place two lenses (made
f + f2
from the same material) a distance L = 1
away from each other. Do this with lenses
2
1 and 3 and then measure the chromatic aberration of this two lens combination. You
may run out of space on your optical rail. If so, you will need to place the two lenses
closer together than optimal. While not optimal, this will still reduce chromatic
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aberration.
Questions
1) What did you observe when you used lens 8 to collimate the light?
2) What is special about an achromatic doublet, such as lens 5, that minimizes
chromatic aberration? How does it work?
f + f2
3) Show that when two lenses of the same material are separated by L = 1
,
2
chromatic aberration is minimized.
4) What are the indices of refraction for each lens, for each wavelength? How does
this compare with the accepted values? Determine A and B (equation 1) for each
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lens.
Department of Physics
Jan. 12 2009
University of Missouri-Kansas City
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Department of Physics
Jan. 12 2009
University of Missouri-Kansas City
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