Diffraction grating and wavelength

[CAH]

Hi I've attached the question and mark scheme,

I don't understand part 6(d)... Why have they used sin90?

nλ=dsinθ

If there is another order beam how can it be known the angel at which it exists from the zero order?
Thanks

 

[mfb]

Why have they used sin90?

That is the largest angle where you can observe anything and it maximizes the sine. Either something is observable at this or a smaller angle, or it is not observable at all.

If there is another order beam how can it be known the angel at which it exists from the zero order?

The 0th order is always at 0 degrees.