Optics question - check me please?

[big_boi]

Homework Statement

A diffraction grating is placed 0.50 m from a screen. The diffraction grating is marked 750 lines/mm. Find the distance between the second order maximum and the first order maximum when light of wavelength 550 nm is passed through the slits.

Homework Equations

The Attempt at a Solution

angle from center = arcsin( m*wavelength*N )

so for m=1 (first order)

angle = arcsin (1*550x10^-9*750/10^-3m) =24.36 degrees

And the distance from center: d = 0.50 meter * tan24.36 = 0.22641 m

Repeat the calculations for m=2:

angle = arcsin (2*550x10^-9*750/10^-3m) =55.59 degrees

And the distance from center: d = 0.50 meter * tan55.59 = 0.72992 m

So their separation = 0.72992 - 0.22641 = 0.5035 m

 

[anathema]

Your solution is correct. The distance between the second order maximum and the first order maximum is 0.5035 m. This is a useful calculation to determine the spacing of the diffraction grating and the wavelength of light being used. Good job!