A) A diffraction grating has 5.7×10 5 slits/m. Find the angular spread in the se

Question

A)
A diffraction grating has 5.7×105 slits/m.
Find the angular spread in the second-order spectrum between red light of wavelength 7.1×107 m and blue light of wavelength 4.6×107 m .

B)
The wings of a certain beetle have a series of parallel lines across them. When normally incident 470-nm light is reflected from the wing, the wing appears bright when viewed at an angle of 52 .

How far apart are the lines? Assume that we see the first diffractive order.


C)
Three (and only three) full spectral orders can be seen on either side of the central maximum when white light with the largest wavelength 750 nm is sent through a diffraction grating.

What is the maximum number of slits per cm for the grating?

Explanation / Answer

d= 1/N = 1/5.7×105 slits/m. = 1.739 * 10^-6 m

d sin theta = m Lamda

theta_r = sin^-1 ( 2 ( 7.1×107 m)/1.739 * 10^-6 m) = 54.74

theta_b = sin^-1 ( 2 ( 4.6 ×107 m)/1.739 * 10^-6 m) = 31.94

del thea = 22.79

---------------------------------------------------------

d = m Lmada/ sin theta = 1 ( 470-nm)/ sin52 = 0.596 * 10^-6 m

(c)

maximum number of slits sin(theta)=1

1/d = N=1/(n*wavelength)=1/(3*750*10^-7) = 4444 /cm

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