Question

The line spectrum of sodium includes a yellow line with lambda1=589.00nm. A certain diffraction grating produces this line, in first order, at theta1 = 25.00 degrees from the central maximum. A second distinct line has lambda2 = 589.59 nm. What is the angular separation between these two lines?

Answer 1

given
diffraction grating with

lambda1 = 589 nm

theta1 = 25 degrees
first order m =1

from the condition d sin theta = m*lambda

   d = m*lambda1/sin theta1

   d = 1*589*10^-9/(sin(25)) m

   d = 1.39369*10^-6 m

   d = 1.39369 micro meters

the second line of wavelength is lambda2 = 589.59 nm

   the angle theta is

  
   sin theta2 = m*lambda2/(d)

   sin theta2 = (1*589.59*10^-9)/(1.39369*10^-6)

   theta2 = arc sin ((1*589.59*10^-9)/(1.39369*10^-6))

   theta2 = 25.02681 degrees

the angular separation is theta = theta2-theta1

   theta = 25.02681- 25.00 degrees

   theta = 0.02681 degrees

the angular separation between these two lines is theta = 0.02681 degrees