Question

Red light of wavelength 633 nm from a helium-neon laser passes through a slit 0.360 mm wide. The diffraction pattern is observed on a screen 3.75 m away. Define the width of a bright fringe as the distance between the minima on either side.
(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) 0.0130 m

b') w' = =6.46*10^{-3] m

Explanation:

given data:

\lambda of light = 633 nm

width of siit a =0.360 mm

distance from screen = 3.75 m

a) the first minima is located at

$sin\theta = \frac{\lambda}{a}$

              =$= \frac{633 *10^{-9}}{.360*10^{-3}}$

           $\theta = 0.100$

$y_1 = dtan\theta_1 = 3.75*tan(0.100) = 6.54 *10^{-3} m$

with of central fringe  = 2y_1 = 2*6.54 *10^{-3} = 0.0130 m

b)

width of the first bright fringe on either side of the central one = $w' = y_2 -y_1$

calculation for y_2

$sin\theta = 2\frac{\lambda}{a}$

              = $= 2*\frac{633 *10^{-9}}{.360*10^{-3}}$

             $\theta = 2*0.100 = 0.200$

$y_2 = dtan\theta_1 = 3.75*tan(0.200) =0.0130 m$

$w' = 0.0130 -6.54 *10^{-3}$

w' = =6.46*10^{-3] m