Question

White light containing wavelengths from 4.10E2 nm to7.50E2 nm falls on a grating with 9.2E3 lines/cm. How wide is thefirst-order spectrum on a screen 2.50 m away?

Answer 1

first get d

       d = 1/N =   1 / 9200 lines per cm   =

           =     1.086957 x 10^-4 cm =    1086.957 nm

Now use

    λ = dsinθ    to get θ for the longest andshortest wavelength

     sinθ = λ /d

for shortest wavelength of 410 nm

     sinθ = 410 /1086.957      θ =   22.16degrees

for longest wavelength of   750 nm

   sinθ = 750 /1086.957        θ =   43.63 degrees

Now get the distance from center for each by usingtangent...

   x = D tanθ

shortest?

   x = 2.50 * tan22.16 =     1.0182 meters

longest?

   x = 2.50 * tan43.63  =   2.3832 meters

width = Δx = 2.3832 - 1.0182 =   1.365 meters