Diffraction is evidence of the wave nature of light.
Diffracting waves interfere after passing through a double slit. The effects of interference can be seen on a screen at a distance beyond the slits.
The mth bright fringe lies where the wave from one slit travels m wavelengths farther than the wave from the other slit.
Using the small angle approximation, we can define the angle of the mth bright fringe.
Using the relationship from the small angle approximation, we can define the position of the mth fringe, defined as the distance from the central maximum.
We can use the difference between the positions of two consecutive fringes to define the fringe spacing.
Destructive interference will occur everywhere we add a half integer of the wavelength. We can use this fact to define the distance from the central bright maximum to the dark fringes.
A laser shining through a double-slit produces a diffraction pattern on a screen that looks like this.
Sample questions
Light of wavelength λ1 illuminates a double slit and interference fringes are seen on a screen. When light of a second wavelength λ2 illuminates the same double slit, with the same screen at the same distance, the fringes are closer together. Which statement is true?
A. λ2 is shorter than λ1
B. λ2 is longer than λ1
C. Cannot be determined from this information
A laser produced a double slit diffraction pattern on a screen. The graph above shows the intensity of the signal as a function of x (in cm). Assume that the distance between the centers of the slits is 0.062 mm, and that the slits are located 0.85 m from the screen.
What is the wavelength (in nm) of the laser?
Intensity of double-slit interference
We can use the amplitude function for two interfering waves, tailored to the double slit scenario, to write a function for amplitude.
We can use the fact that intensity goes as amplitude squared to write a function for the intensity of double slit diffraction. The final form writes intensity Idouble in terms of the intensity I1 = ca2 at the screen due to one wave, using a proportionality constant c.
A diffraction grating is similar to a double slit, but with many more slits. This diagram shows ten slits (or lines) but a typical diffraction grating can have hundreds or thousands of slits.
Each slit increases the amplitude of the light, so for N slits, the intensity goes as N2 times the intensity of the light from one slit.
Interference increases intensity of bright fringes by a factor of N. Energy is conserved, so the bright fringes tend to become very narrow.
Practice problem
Different wavelengths of light diffract by different degrees. Long wavelengths of light diffract more than short wavelengths. This makes diffraction gratings very useful for analyzing the wavelengths that make up a particular sample of light.
Light that is created from glowing gases carries characteristic wavelengths of light associated with photons emitted from excited electrons dropping to lower states. The wavelength of light corresponds to the difference in energy of the electron states. The light signature can be analyzed using a diffraction grating to identify the constituent elements in a gas.
Diffraction gratings are commonly used by astronomers to identify the elements that are present in stars.
The separation of light reflecting from a DVD arises from the light being diffracted by the many grooves on its surface.
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