Problem $2.$ You are asked to design a di$$raction grating that will disperse the first$-$ordervisible

spectrumthroughanangularrangeof $27\mathrm{.}0$ whenwhitelightisshoneonthegrating.

$($a$)$ At what angles will the first order spectrum begin and end? $($Use the identity sin$($$+$ $)$

sin cos $+$ cos sin and consider the ratiosin$($$+$ $)/$sin to solvefor $.)$

$($b$)$ Howmanylinesper millimetermustthe gratinghave?

$($c$)$ Will the full second$-$order visible spectrum appear in the di$$raction pattern for this grat$-$

ing?