PHY 212 Laboratory for 4/13/2004

Spectroscopic Analysis of an Incandescent Bulb

The spectroscope attachments for the force tables will be used with a diffraction grating to determine some of the details of our perceptions of the continuous visible spectrum produced by an incandescent source.

Setup

The spectroscope consists of a slit which allows a narrow beam of white light to pass through a diffraction grating at the center of the table. The grating will spread the light into a spectrum which can be seen through the pivoting telescope on the opposite side. The wavelength (l) can be determined from the expression

d sin q = ml

where d is the spacing between the lines of the grating, q is the angle between the perpendicular to the grating and the maxima at which the telescope is located, and m = 1,2,3, ... (You will calculate the spacing from the grating specifications, typically listed in the form of lines per inch or lines per mm.)

Procedure and Report

  1. From the first order (m = 1) diffraction, each member of the group will

    1. determine the wavelength of their visual threshold at both the violet and the red end of the spectrum, and
    2. determine the wavelength at the center of the red/green (yellow), and the blue/violet (cyan) transition bands. Some students may see a wide yellow band while others will see a very narrow band. Some may see a sharp division between green and blue while others will see a more gradual blending through a blue-green region. Be sure to record a qualitative description of how each of these two regions appear to you.

  2. Measure the angle for the second order diffraction (m = 2) of the yellow band and verify that it yields the same wavelength as the calculations for first order.
[NOTE: In all cases, record the angle on both sides of the perpendicular and average the results. This will compensate for any misalignment of the apparatus.]

  1. Color vision starts with the retina, which has three "cone" cells sensitive to a limited range of frequencies centered on the red, green, and blue regions respectively. The response curves (plots of cell response vs. wavelength) are roughly bell-shaped and overlap to varying extents. The example shown would represent the case in which the student sees a very narrow yellow band (both the red and green cones must be stimulated), but a very gradual transition from green to blue. Sketch the three response curves for your eyes based upon your calculations above. While the sketches are quantitative, the tails of the red and blue curves and the overlap regions should reflect your personal data. (Note: This is an oversimplification of color interpretation that also involves higher level processing in the brain. )

Width of a Hair from Diffraction

You will determine the width of a human hair taken from your head by diffracting the light of a He-Ne laser with the hair. When the hair is place in font of the beam, the beam is diffracted in the same manner as with single slit diffraction. The minima for single slit diffraction is given by

a sin q = ml

where a is the width of the slit, q is the angle between the perpendicular to the slit and the minima, and m = 1,2,3, ...

Babinet's Principle states that the diffraction pattern created by single slit opening is exactly the same as that for a barrier of the same dimensions. That is, the hair will create the same diffraction pattern as a single slit of the same width. Hence, we can use the formula above, with the width of the hair taking the place of "a", the slit width.

Setup

  1. Place the laser on a level table and aim it such that the beam strikes a flat screen or surface approximately 1 meter away.

  2. Cut a 1" square hole in a stiff card, such that the laser beam will pass through the hole when the card is resting on the table.

  3. Tape the hair across the hole in a vertical orientation. (If your hair is shorter than about 1", you may ask a fellow lab student to "borrow" a hair.)

Procedure and Report

  1. Place the card in front of the laser, such that the hair intercepts the laser beam. You should see a clear diffraction pattern on the screen.

  2. You will be able to determine the sine of the angle by making the following measurements.

    1. Measure the distance from the hair to the screen.
    2. Measure the distance between the first order (m=1) minima on either side of the central maxima. If possible, measure the distance between the second order (m=2) minima, as well.

  3. Apply the expression above to find the width of the hair. You may use small angle approximations in determining the sine of the angle from the distances measured. But keep in mind that q in the formula above is the angle from the center of the central maxima to the minimum on either side.