An 18-mm-wide diffraction grating has rulings of 710 lines per millimeter. monochromatic light of wavelength 506 nm wavelength i

Question

4 years ago

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An 18-mm-wide diffraction grating has rulings of 710 lines per millimeter. monochromatic light of wavelength 506 nm wavelength i

s incident normally on the grating. what is the largest angle from the centerline at which an intensity maximum is formed?

Physics

1 answer:

aliina [53] · Answer 1 · 2022-01-16T01:41:25+03:00

W= 18*10^-3m
N= 18*710 ( because you have 710 slits per mm ) = 12780
lambda = 506*10^-9

The first step is to workout d.
d = w/N
d =18*10^-3m/12780
d =1.41*10^-6m

The second step is to work out the maximum number of m.
Since sin (theta) = less than 1, then m*lambda/d = less then 1,
therefore m= less than d/lambda
( I know thats confusing but trust me )
so m is less than 1.41*10^-6m/506*10^-9
= 2.7
Therefore use m = 2

Lastly put it all into the formula
dsin (theta) = m*lambda so:
theta = sin^-1(m*lambda/d)
theta = sin^-1(2*506*10^-9/1.41*10^-6m)
theta = 45.95 degrees or 46 degrees