Answer to Question #214746 in Optics for lala

Question

1. The bright central fringe in a single-slit diffraction pattern from the blue light of wavelength 476 nm is 2.0 cm wide on a screen that is 1.05 m from the slit.

(a) Without calculating the slit width, determine the width of first-order bright fringe.

(b) How wide is the slit?

(c) If the blue light is replaced with monochromatic red light, what is the effect on the width of the bright central fringe? Briefly justify your answer

Answer 1

Gives

D=1.05cm

2x=2.0cm

$\lambda=476nm$

We know that

$asin\theta=m\lambda$

Central bright fringe m=-1to m=+1 extends

$asin\theta=m\lambda$

$$tan\theta=\frac{x}{D}$$

$$x_1=\frac{m\lambda D}{a}=\frac{2\times4.76\times10^{-7}\times1.05}{5\times10^{-5}}=2cm$$

$a=\frac{m\lambda}{sin\theta}=\frac{m\lambda D}{x}$

$a=\frac{1\times4.76\times10^{-7}\times1.05}{0.01}=5\times10^{-5}m$

Blue light replace by red light

$\lambda_R=6800A$

$$x_1=\frac{m\lambda D}{a}=\frac{2\times6.8\times10^{-7}\times1.05}{5\times10^{-5}}=2.85cm$$

Difference x'=2.85cm-2.0cm=0.85cm