Inquiry: Measuring by Diffraction
Purpose: In this Inquiry you will apply the principles of diffraction of light.
According to Huygen's principle, every point on a light wave front may be considered as a new source of light. In general, all parts of each new wavelet are cancelled due to destructive interference except that part traveling in the same direction as the original wave front. When a diffraction grating is placed in the path of a plane wave front only alternate parts of it pass through. The ruled lines are opaque to the light and the uniform spacings between the lines, being transparent to the light, provide a large number of line transmission slits very close together. The new wavelets originating at the slits interfere in such a way that several new wave fronts are set up, one traveling in the original direction and the others at various angles from this direction depending on the wavelength. If a narrow slit is illuminated by white (polychromatic) light and viewed through a transmission grating, a white image of the slit will be seen directly in line with the slit opening and pairs of continuous spectra will be seen equally spaced on opposite sides of the slit opening. The first pair is known as the first order images, the second pair as second order images and so on. From the geometry of the interference pattern of the light going through the openings you should be able to show the following equation for the wavelength of the light:
where n = the order of the image. The angle can be found in the diagram above by realizing that the tan Θ = distance from the center image to the nth image (x) divided by the distance from the diffraction grating to the screen (L).
Part 1: Grating Constant:
Mount the scale and slit on one end of the optical bench and illuminate the slit with white light. Mount the grating near the opposite end of the optical bench and with your eye close to the grating observe the first-order image. Locate a rider on the meter stick at the yellow part in each first order spectrum. Using the wavelength of yellow light 5800 Angstroms compute the diffraction grating in lines/inch.
Part 2: Range of the visible spectrum:
Examine a first-order continuous spectrum and place riders on the scale at the extreme blue and extreme red ends of the spectrum. Using the known grating constant, compute the upper and lower limits of the visible spectrum.
Part 3: Wavelengths of Gas Lights:
Calculate the wavelengths of the two brightest spectral lines that emit from Neon gas. Exchange the gas tubes to look at other "finger print" spectral emissions from various gases.
Part 4: Wavelength of laser light:
Mount a know diffraction grating in a laser beam to calculate the wavelength of the laser light and a percent error.
Part 5: Diameter of a Hair:
Mount a hair on the mount provided by the use of tape. Place the hair in the laser beam and on the wall measure the distance from one nth order dark line to the same nth order dark line on the other side and divide by two. This means that our n will be an order plus 0.5 because these are points of destructive interference. Determine the width of the hair.
Part 6: Width of slit:
Place a commercial single slit in the laser beam and observe the diffraction pattern. Make the necessary measurements to determine the width of the slit.
Part 7: CD, DVD & Blue-Ray grooves:
Shine a laser beam through a CD which has it's backing scraped off to get the diffraction pattern. Determine the spacing between grooves on the CD. The theoretical spacing is 1750 nm. Try the DVD. What about a Blue-Ray disc?