Question

When “white light” which contains all the colors goes into a grating, it is separated out into the spectrum from 400. to 700. nm.     The first order is distinct, in that, for m = 1, the colors range from violet to red with no “m = 2” colors in that range.    However, as m increases, the orders DO overlap.   What is the smallest value of m for which the red appears at a larger angle than the violet of the next (m+1) order? If you calculated all possible angles in Question 2, you can simply look and see (you could draw on a paper that violet to red ranges from, say, 33 to 45 degrees, and the next order goes from 42 to 59 – whatever your data shows. (I made up these angles, by the way, so don’t expect them to fit your data. (5)

Answer 1

with diffraction

a Sin = m

for red Sin_r = m _r

for violet Sinv = m v  

we want the red of the first order to appear at a larger angle than the violet of the next order i.e m+1

Sin_r / Sinv = m/m+1 * _r /_v = 700m/400(m+1) >1

7m > 4(m+1) or

3m >4

lowest value of m = 2

the second order red appears after the 3rd order violet, i.e. the two overlap.