15.3. Diffraction Gratings http://www.ck12.org
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Also in this image is the measurement forθ, which can be used to calculate the wavelength of the original light
source. The equation from the double slit experiment can be adjusted slightly to work with diffraction gratings.
Whereλis the wavelength of light,dis the distance between the slits on the grating, andθis the angle between the
incident (original) light and the refracted light,
λ=xdL =dsinθ(Note thatLx=sinθ, using the small angle approximation theorem.)
Looking at the equation,x=λdL, it should be apparent that as the distance between the lines on the grating become
smaller and smaller, the distance between the images on the screen will become larger and larger. Diffraction
gratings are often identified by the number of lines per centimeter; gratings with more lines per centimeter are
usually more useful because the greater the number of lines, the smaller the distance between the lines, and the
greater the separation of images on the screen.
Example Problem:A good diffraction grating has 2500 lines/cm. What is the distance between two lines on the
grating?
Solution:d= 25001 cm− 1 = 0. 00040 cm
Example Problem:Using a diffraction grating with a spacing of 0.00040 cm, a red line appears 16.5 cm from the
central line on the screen. The screen is 1.00 m from the grating. What is the wavelength of the light?
Solution:λ=xdL =(^0.^165 m)(^4.^0 ×^10
− (^6) m)
- 00 m =^6.^6 ×^10
− (^7) m
Summary
- Diffraction gratings can be made by blocking light from traveling through a translucent medium; the clear
places behave as slits similar to the slits in a double slit experiment. - Diffraction gratings form interference patterns much like double slits, though brighter and with more space
between the lines. - The equation used with double slit experiments to measure wavelength is adjusted slightly to work with
diffraction gratings.λ=xdL=dsinθ