Question

500 nm light passes through a circular aperture that has a diameter d = 30.0 μm. A diffraction pattern forms on a screen 350 mm from the aperture. Calculate the area of the central bright fringe.

Answer 1

Complete Ques

Answer:

The value is $A = 0.00214 \ m^2$

Explanation:

From the question we are told that

    The wavelength is  $\lambda = 500 \ nm = 500 *10^{-9} \ m$

     The diameter of the aperture is $d = 30 \mu m = 30*10^{-6} \ m$

     The distance of the screen from the aperture is $D = 350 \ m m = 0.350 \ m$

Generally the distance from the center the the edge of the central bright fringe is magmatically reparented as

          $y = \frac{m * \lambda * D}{d}$

Generally m =  1 because after the central bright fringe we have the first order fringe

So

          $y = \frac{1 * 500 *10^{-9} * 0.350}{30*10^{-6}}$

=>       $y =0.00583 \ m$

Generally the area of the central bright fringe

           $A = 2 \pi * y^2$

=>        $A = 2 * 3.142 * 0.00583^2$

=>        $A = 0.00214 \ m^2$