Diffraction Occurs When Light Waves Interfere with Each Other. a Diffraction Grating Consists

Diffraction

Introduction Diffraction occurs when light waves interfere with each other. A diffraction grating consists of a thin piece of opaque glass or plastic with a pattern of equally-spaced, transparent slits. If a beam of monochromatic light (that is, light of only one wavelength) is incident on a diffraction grating at 90°, then a series of bright and dark bands (called fringes) will emerge. The location of the bright bands is given by the diffraction grating equation:

dsinθ = mλ (m = 0, 1, 2, ...)

The variable d is the distance between the centers of the grooves in the diffraction grating, θ is the angle between the line connecting the center of the grating and the bright band and the line perpendicular to the grating, m is the order of the band, and λ is the wavelength of the light.

Notice that the angle of diffraction (θ) depends on the wavelength. Red light (longer wavelength) is diffracted through a larger angle than blue light (shorter wavelength). This means that a diffraction grating can spread polychromatic light (that is, light of more than one wavelength) into its component colors. This turns out to be very useful because most natural light sources emit light of more than one color.

The color content (or wavelength) of light is called its spectrum. The spectrum is directly related to the structure of the atoms or molecules that produced it. Therefore, spectral measurements are very useful to physicists. A device capable of measuring the spectrum of a light source is called a spectrometer. One way to make a spectrometer is by using a diffraction grating as discussed above. Another way is by using a glass prism which operates on the basis of refraction. There are also other ways to make a spectrometer.

The purpose of this lab is to test the diffraction grating equation.

Experimental Procedures

Theoretical Analysis

1) The distance between the diffraction grating and the aperture is L and the horizontal distance between the aperture and a bright band is x. Derive a trigonometric expression for sinθ (not θ itself) in terms of x and L. Manipulate this equation until x and L each appear only once. Hints: (1/x)/sqrt(1/x2) = 1, so it is within the rules of algebra to multiply by this value. Also, sqrt(a)*sqrt(b) = sqrt(a*b).

2) Using Snell's law of diffraction and your equation from step 1, derive an equation for λ in terms of the measurable quantities m, d, L, and x. Check your equation with your instructor.

Polychromatic Light

1) Use a spectroscope with 300 grooves/mm. Calculate the distance between grooves, d, for this spectroscope.

2) View and record the position (x) of the upper limit (edge of rusty red) of the continuous spectrum produced by white light (either from outside or the “universal light source”). Don’t subtract.

3) Use the formula developed in the theoretical analysis section to calculate the wavelength of this light. 4) View and record the position (x) of the lower limit (edge of deep purple) of the continuous spectrum produced by white light. Don’t subtract. 5) Use the formula developed in the theoretical analysis section to calculate the wavelength of this light. 6) Compare your results to the accepted values of approximately 400 and 700 nm. Note that the human vision system can sense light with wavelengths of 312 nm and 1050 nm, but the sensitivity is 1/1000

that of the normal range.1 7) Repeat steps 1 through 6 above using a spectroscope with 600 grooves/mm. Don’t subtract.

Emission Spectrum

1) Look at one of the gas tubes without a spectroscope. Record its apparent color. 2) Use a spectroscope with 600 grooves/mm. Line up the aperture at the back of the spectroscope with the gas tube. Record the location (x), color, width (sharp or fuzzy), and relative intensity (bright or faint) for each line. Don’t subtract. 3) Calculate the wavelength for each line and compare to the following table with the accepted values for

the most prominent lines.2 You might observe lines that are not listed in the table or you may miss a line that is in the table. Don’t subtract. 4) Identify the element, if possible. If you don’t think that an element is one of the five mentioned below, then state this in your conclusion. 5) Repeat steps 1 through 4 with the other available tubes. Don’t subtract.

Element Wavelength (nm) Color Comment Helium 388.9 Violet Faint 447.1 Indigo 501.6 Green u.6 Yellow-Orange 667.8 Red 706.5 Dark Red Faint Hydrogen 410.0 Violet Faint 434.0 Indigo 486.1 Light Blue 656.3 Red 2 lines Krypton 427.4 to 484.7 Blue Spread 557.0 Yellow-Green u.0 Orange Mercury 435.8 Indigo 546.1 Yellow-Green 567.5 to 580.3 Yellow 5 lines Neon is a case where the lines are so rich that it is more the absence of certain colors rather than the presence of specific lines that gives away its presence. This is in the range of 490 to 530 nm.

1 Hecht, Physics, 3rd edition, Thomson Brooks/Cole, 2003, pg. 800 2 Weast, CRC Handbook of Physics and Chemistry, 60th edition, CRC, 1980