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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).

From the lens maker’s equation:

€

1f

= (nl −1)(1R1−1R2) and knowing that n=n(λ), one

concludes that the focal length, f, of a simple lens is a function of wavelength, f=f(λ).

Since,

€

1so

+1si

=1f

the image distance will also be a function of wavelength, resulting in a

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:

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n(λ) = A +Bλ2

+Cλ4

(1)

Often, the first two terms are sufficient, thus knowing the index of refraction at 2 wavelengths is sufficient to obtain n(λ). 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.

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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.

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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.

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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

from the same material) a distance

€

L =f1 + f22

away from each other. Do this with lenses

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 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?

3) Show that when two lenses of the same material are separated by

€

L =f1 + f22

,

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 lens.

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