physics wavelength question, please help :)

Question

A diffraction grating with line spacing of 2531 lines per cm creates its first bright spot 9.4 degrees from the central bright spot. Find the wavelength of the line illuminating the diffraction grating.
Provide your answer in nanometers. You may have to change the units to convert your answer to nm.
 Keep at least three significant figures while calculating your answer.

 

thanks so much!!

Answer 1

This looks like a problem where you have to use

 

nλ = d sinθ

 

n = 1

d = (1 cm) / 2531 = 3.951 x 10^-4 cm

sinθ = sin9.4° 

 

λ = (3.951 x 10^-4 cm) sin9.4° = 6.453 x 10^-5 cm

 

You can convert cm to nm (1 nm = 10^-9 m).  The equation at the top may be used for a similar problem that you posted.