1. What is the angular separation of two spectral lines of wavelengths 439 nm an

Question

1. What is the angular separation of two spectral lines of wavelengths 439 nm and 395 nm formed in order m=2 with a 367 line/mm grating? Express the answer in degrees with two decimal places.

2. A diffraction grating has a grating spacing of 2,130 nm. If a light ray of a wavelength 591 nm is incident perpendicularly upon the grating, what angle (in degrees) will you see the second order diffraction spots at?

Express the answer with one decimal place.

3. A diffraction grating has a grating spacing of 2,045 nm. If a light ray of a wavelength 471 nm is incident perpendicularly upon the grating, what angle (in degrees) will you see the first order diffraction spots at?

Express the answer with one decimal place.

Explanation / Answer

1) m lambda = d sin theta

theta = arcsin(m lambda /d) = arcsin(2*439E-9/(1.0E-3/367))=18.8

at other wavelength
theta = arcsin(2*367E-9/(1.0E-3/367))=15.63

d theta = 18.8-15.63=3.17 degrees

2) m lambda = d sin theta
theta =arcsin(2*591E-9/(2130E-9))=33.71 degrees

3) theta = arcsin(1*471E-9/(2045E-9))=13.32 degrees

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