p37_037.pdf

10 − 6 m.

(b) Minima of the single-slit diﬀraction pattern occur at angles θ given by a sin θ = mλ ,where a is

the slit width. Since the fourth-order interference maximum is missing, it must fall at one of these

angles. If a is the smallest slit width for which this order is missing, the angle must be given by

a sin θ = λ . It is also given by d sin θ =4 λ ,so a = d/ 4=(6 . 0 × 10 − 6 m) / 4=1 . 5 × 10 − 6 m.

order that is diﬀracted toward the screen. The condition is the same as m<d/λ and since

d/λ =(6 . 0

10 − 9 m) / 0 . 1=6 . 0

10 − 9 m) = 10 . 0, the highest order seen is the m = 9 order. The fourth

and eighth orders are missing, so the observable orders are m =0,1,2,3,5,6,7,and9.

10 − 6 m) / (600

37. (a) Maxima of a diﬀraction grating pattern occur at angles θ given by d sin θ = mλ ,where d is the slit

separation, λ is the wavelength, and m is an integer. The two lines are adjacent, so their order

numbers diﬀer by unity. Let m be the order number for the line with sin θ =0 . 2and m +1bethe

order number for the line with sin θ =0 . 3. Then, 0 . 2 d = mλ and 0 . 3 d =( m +1) λ . We subtract the

ﬁrst equation from the second to obtain 0 . 1 d = λ ,or d = λ/ 0 . 1 = (600