Question

A scientist shines a beam of white light through a diffraction grating (with 500linesmm), producing a diffraction pattern. The spectrometer only looks at the m=1 bright spot! (The m=2 spectrum will not fit in the view.)

a) Calculate the distance d between individual slits (also called “lines”).

b) The white light spreads into its component colors. For red light (=700nm), what is the diffraction angle θR (in degrees)?

c) For violet light (=400nm), what is the diffraction angle θV (in degrees)?

Answer 1

a) Given that the diffraction grating is of 500lines/mm

So the width of each slit will be

  

Width of the slit will be equal to the distance between individual slits because the slit width is same for every slit in a difraction grating.So the distance between the slits is 210-6m

b) Given wavelength For red light,

We know that equation for bright spot is,

By substituting we get,

  

  

  

so difraction angle for red light   o

c) Given wavelength for violet light

We know that equation for bright spot is

   

Substituting the values we get,

  

  

  

  So diffraction angle for violet light  o