Question

Red light of wavelength 633 nmnm from a helium-neon laser passes through a slit 0.400 mmmm wide. The diffraction pattern is observed on a screen 2.90 mm away. Define the width of a bright fringe as the distance between the minima on either side.

Required:
a. What is the width of the central bright fringe?
b. What is the width of the first bright fringe on either side of the central one?

Answer 1

Answer:

a

 $y_1 = 0.004589 \ m$

b

 $y_2 =0.009179 \ m$

Explanation:

From the question we are told that

   The wavelength of the red light is  $\lambda _r = 633 \ nm = 633 *10^{-9} \ m$

    The width of the slit is  $d = 0.40 mm = 0.40 *10^{-3} \ m$

    The distance of the screen from the point of diffraction is $D = 2.9 \ m$

Generally the width of the central bright fringe is mathematically represented as

       $y_1 = \frac{\lambda * D}{d}$

=>    $y_1 = \frac{633 *10^{-9} * 2.90 }{0.40 *10^{-3}}$

=>    $y_1 = 0.004589 \ m$

Generally the width of the first bright fringe on either side of the central one is mathematically represented as

     $y_2 = 2 * y_1$

=>   $y_2 = 2 * 0.004589$

=>   $y_2 =0.009179 \ m$