7.5 Diffraction of Light Waves
215
same direction, they will cause constructive interference. After the two waves pass
each other, they appear in the water as they did before arriving at the interference
region.
As we observed, the standing wave in a guitar string can be thought of as
two traveling waves of equal amplitude and frequency, but traveling in opposite
directions. The two waves interfere to make nodes where complete destructive
interference occurs.
According to Maxwell’s Theory of Electromagnetism, light waves and all other
kinds of electromagnetic waves obey the linear superposition principle in regions
where the electric permittivity and magnetic permeability are independent of the
strength of the electric or magnetic fields, such as in a vacuum.
7.5 Diffraction of Light Waves
Diffraction is the bending of waves around corners and other barriers. We ordinarily
do not observe the diffraction of light waves through windows because the size of the
diffraction angle depends on the wavelength of the wave divided by the size of the
window. But with tiny openings of a few microns in width, diffraction of visible light
is evident. Biologists who look through microscopes at small objects also see the
effect as diffraction patterns around tiny structures. An optical spectrometer takes
advantage of diffraction to separate light into component frequencies and measure
the corresponding light wavelengths.
A ‘diffraction grating’ is a surface used to spread in angle the various frequencies
of a wave. It does this by diffracting the wave with a grating, a surface with parallel
groves or dark lines separated by distances comparable to the wavelength of wave
being used. It is straightforward to show that light of wavelength λ which arrives
perpendicular to a diffraction grating with spacing between groves of d will be
diffracted to angles
θ m = arcsin
m
λ
d
(7.12)
where m is an integer.
Diffraction gratings have largely replaced prisms in optical spectrometers as they
physically take less space and the separation of frequencies is wider, more uniform
and more easily controlled by the grating construction.
For two point-like sources emitting light at wavelength λ observed with an
instrument with circular aperture of diameter d, the Rayleigh criterion,
sin R > 1.220
λ
d
,
(7.13)
215
same direction, they will cause constructive interference. After the two waves pass
each other, they appear in the water as they did before arriving at the interference
region.
As we observed, the standing wave in a guitar string can be thought of as
two traveling waves of equal amplitude and frequency, but traveling in opposite
directions. The two waves interfere to make nodes where complete destructive
interference occurs.
According to Maxwell’s Theory of Electromagnetism, light waves and all other
kinds of electromagnetic waves obey the linear superposition principle in regions
where the electric permittivity and magnetic permeability are independent of the
strength of the electric or magnetic fields, such as in a vacuum.
7.5 Diffraction of Light Waves
Diffraction is the bending of waves around corners and other barriers. We ordinarily
do not observe the diffraction of light waves through windows because the size of the
diffraction angle depends on the wavelength of the wave divided by the size of the
window. But with tiny openings of a few microns in width, diffraction of visible light
is evident. Biologists who look through microscopes at small objects also see the
effect as diffraction patterns around tiny structures. An optical spectrometer takes
advantage of diffraction to separate light into component frequencies and measure
the corresponding light wavelengths.
A ‘diffraction grating’ is a surface used to spread in angle the various frequencies
of a wave. It does this by diffracting the wave with a grating, a surface with parallel
groves or dark lines separated by distances comparable to the wavelength of wave
being used. It is straightforward to show that light of wavelength λ which arrives
perpendicular to a diffraction grating with spacing between groves of d will be
diffracted to angles
θ m = arcsin
m
λ
d
(7.12)
where m is an integer.
Diffraction gratings have largely replaced prisms in optical spectrometers as they
physically take less space and the separation of frequencies is wider, more uniform
and more easily controlled by the grating construction.
For two point-like sources emitting light at wavelength λ observed with an
instrument with circular aperture of diameter d, the Rayleigh criterion,
sin R > 1.220
λ
d
,
(7.13)