Question

A light source of 460 nm wavelength illuminates a single slit of width 2.80×10−2 mm , producing a standard diffraction pattern on a screen, in which the intensity is 1.03×10−4 W/m2 at the very center of the pattern (θ= 0∘). At a point on the screen for which θ = 1.20 ∘, determine the intensity. Express your answer to three significant figures and include the appropriate units.

Answer 1

`3.6* 10^(-6)W/m^2`

Step-by-step explanation:

Given,

Wavelength of the light, λ = 460 nm =460 ×10⁻⁹ m

Slit width, a = 2.80 ×10⁻² mm = 2.80 ×10⁻⁵ m

Intensity at the center of the pattern, I₀ = 1.03×10⁻⁴ W/m²

We need to find the intensity at a point for which θ = 1.20°

`I = I_o((sin\beta)/(\beta))^2`

where
`\beta = (\pi a sin \theta)/(\lambda)`

first, calculate the value of β

`\beta = (\pi * 2.80 * 10^(-5) sin 1.20^o)/(460 * 10^(-9))=4`

`I =1.03* 10^(-4)* ((sin 4)/(4))^2=3.6* 10^(-6)W/m^2`