Red light with a wavelength of 725 nm shines through a single slit, and forms a pattern on a screen placed 1.25 m away. if the width of the slit is 18.5 micrometers, find the width of the central maximum

(a) in degrees and (b) in centimeters

(a) 4.5°     (b) 9.8 cm

Explanation:

Given:

λ = 725*10^(-9) m

d = 18.5*10^(-3) m

L = 1.25 m

Let θ₁ be the first minimum and is equal to = λ /d

= 725*10^(-9)/18.5*10^(-6)

= 0.0392

= 0.0392

In view of smallness of this number, we have sin θ₁ = θ₁ = 0.0392

The angular width of the central maximum θm is twice the first minimum.

so θm = θ₁ = 2*0.0392 = 0.0784

The angular width in degrees is then 360*θm/2π = 4.5°. The width in centimetres is proportional to the distance to the screen (L = 125 cm) and is given approximately by θm*L = 0.0784*125 = 9.8 cm