Diffraction Gratings - N narrow slits

[bobpeg123]

A grating having 600 lines per mm is illuminated with sodium light of mean wavelength
589.3 nm. Determine the maximum order of diffraction that can be observed. By
differentiating the expression: d sin θ = m λ, calculate the angular separation in arc minutes
in second order for the two wavelengths 589.0 and 589.6 nm.


For the first part of the question: The first thing I've done is assumed a value of m = 1, and therefore found θ = 20.71 degrees.

I've tried searching for how to use this information to find the maximum order but it just brings up d sin θ = m λ and I'm not sure how to use this to calculate the maximum order.

Also, for the second part, does that want me to differentiate with respect to t? I'm completely unsure how to start it.

 

[kuruman]

I've tried searching for how to use this information to find the maximum order but it just brings up d sin θ = m λ and I'm not sure how to use this to calculate the maximum order.

You have d sin θ = m λ. Look at the right side; it increases as m increases. Can it increase forever? If not, what is its limiting value and why?

Also, for the second part, does that want me to differentiate with respect to t? I'm completely unsure how to start it.

If by t you mean θ, the answer is yes. I suggest that you calculate the differentials on each side.