WEBVTT
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This is College Physics Answers
with Shaun Dychko.
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Structures on a bird feather act like
a diffraction grating that reflects
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with 8,000 lines per centimeter.
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And the first order maximum
is what we want to find.
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What is the angle to the first
order of maximum
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given a wavelength that's incident
to 600 nanometers.
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So the separation between the,
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we wouldn't call them slits because
the light is not transmitting through
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the diffraction grating in this
case it's reflecting off.
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So you might see these scratches
in the structure
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and the separation between each scratch
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is gonna be one time state of the minus
two meters that's one centimeter
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for every 8,000 lines.
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And this means there is one in
a quarter micrometers
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between each line that's 1.25 times ten to
the minus six meters between each line.
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We want to know the first order of maximum,
so *m* is one
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and the wavelength is 600 nanometers
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and this formula, we can solve for theta
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by dividing both sides by *d*
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and then take the inverse
sine of both sides.
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So the angle is going to be the inverse
sine of the order times the wavelength
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divided by the separation between the cuts.
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So that's inverse sine of the order of one
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times 600 times ten to
the minus nine meters
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divided by 1.25 times ten
to the minus six meters
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giving an angle of 28.7 degrees
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to the first order of maximum
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with 600 nanometer wavelength light.