Question

The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are 656 nm(red) and 486 nm (blue). Light from a hydrogen lamp illuminates a diffraction grating with 520lines/mm , and the light is observed on a screen 1.5m behind the grating.
What is the distance between the first-order red and blue fringes?
Express your answer to two significant figures and include the appropriate units.

Answer 1

Answer:

0.152 m

Explanation:

The condition for constructive interference is

d sinθ= mλ  (m= 0,1,2,3...)

the slit width

d= 1/N

d= 10^(-3)/520

= 1.92×10^(-6)

The angular spread for the red light is

$\theta_r= sin^{-1}(\frac{m\lambda}{d})$

$\theta_r= sin^{-1}(\frac{656\times10^{-9}}{1.92\times10^{-6}})$

= 19.97°

The angular spread of blue light is

$\theta_b= sin^{-1}(\frac{m\lambda}{d})$

$\theta_b= sin^{-1}(\frac{456\times10^{-9}}{1.92\times10^{-6}})$

=14.66°

The distance between the first order red fringe and blue fringe is,

y= y_r- y_b = Ltanθ_r -Ltanθ_b

=1.50( tan19.97°-tan14.66°) = 0.152 m