A transmission diffraction grating with 420 lines/mm is used to study the light intensity of di event orders (n). A screen is located 2.8 m from the grating. What are the positions on the screen of the three brightest red lines for a hydrogen source?

Diffraction grating is used to form interference pattern of dark and bright band.

Distance between adjacent slits (a) = 1 / 420 mm

= 2.38 x 10⁻³ mm

2.38 x 10⁻⁶ m

wave length of red light

= 680 x 10⁻⁹ m

For bright red band

position x on the screen

= n λD / a, n = 0,1,2,3 etc

D = distance of screen

putting n = 1, 2 and 3, we can get three locations of bright red band.

x₁ = λD / a

= 680 x 10⁻⁹ x 2.8 / 2.38 x 10⁻⁶

=.8 m

= 80 cm

Position of second bright band

= 2 λD / a

= 2 x 80

= 160 cm

Position of third bright band

= 3 λD / a

= 3 x 80

= 240 cm