Question

A 500 lines per mm diffraction grating is illuminated by light of wavelength 510 nm. What is the angle of each diffraction order?

Answer 1

there are three diffraction orders. Their angles are: 14.8, 30.7, 49.9

Answer 2

But I shall mention it anyway:
n ? = d sin(?)

where ? is the angle of emergence, d is distance between slits, ? is the wavelength of the light, n is diffraction order.

all the best!

-EDIT-
alright, since you 'suck' at physics [come on, you can do it if you really think you can], I'll work out some bits for you.

first, sub in your values.
500 lines per mm means 500 000 lines per m
so the distance between each slit is 0.000002 m = 2 x 10^-6 m. always use SI units.

let's do order 1 first. easiest.

your wavelength is 510nm = 5.1 x 10^-7 m

so what is your equation?

sub in the values and work it out!

bring sin? to one side, so you get sin? = something.
then function sin^-1 to your value for sin?. you will get your ?.

all the best!