Question

After a laser bean passes through two thin parallel slits, thefirst completely dark fringes occur at ± 15.00with the original direction of the beam, as veiwed on a screen farfrom the slits.
(a) What is the ratio of the distance between the slits to thewavelength of the light illuminating the slits?
(b) What is the smallest angle, relative to original directionof the laser beam, at which the intensity of the light is 1/10 themaximum intensity on the screen?

Answer 1

Answer:

143 °

Explanation:

a ) If d be the distance between slits , λ be wavelength of light used and at angle θ nth dark fringe is formed then

d sinθ = ( 2n+1) λ/2

for first dark fringe

d sinθ = λ/2

d /λ = 1/ 2 sinθ

1 / 2 sin15

= 1.93

b )

For intensity of fringe at angle θ,  the relation is

I = I₀ cos²θ

I / I₀  = cos²θ/2

Given I / I₀ =0. 1

0.1 = cos²θ/2

θ/2 = 71.5

θ = 143 °