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

Answer:

$3.6\times 10^{-6}W/m^2$

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°

$I = I_o(\frac{sin\beta}{\beta})^2$

where $\beta = \frac{\pi a sin \theta}{\lambda}$

first, calculate the value of β

$\beta = \frac{\pi \times 2.80 \times 10^{-5} sin 1.20^o}{460 \times 10^{-9}}=4$

$I =1.03\times 10^{-4}\times (\frac{sin 4}{4})^2=3.6\times 10^{-6}W/m^2$