Question

As an admirer of Thomas Young, you perform a double-slit experiment in his honor. You set your slits 1.19 mm apart and position your screen 3.53 m from the slits. While Young had to struggle to achieve a monochromatic light beam of sufficient intensity, you simply turn on a laser with a wavelength of 635 nm. How far on the screen are the first bright fringe and the second dark fringe from the central bright fringe? Express your answers in millimeters.

Answer 1

Answer:

First bright fringe is at 1.82 mm

First dark fringe is at 2.83 mm

Solution:

As per the question:

Slit width, d = 1.19 mm = $1.19\times 10^{- 3}\ m$

Distance from the screen, x = 3.53 m

Wavelength of the light, $\lambda = 635\ nm = 635\times 10^{- 9}\ m$

Now,

We know that the 1st bright fringe from the central fringe is given by:

$y = \frac{n\lambda x}{d}$

where

n = 1

$y = \frac{1\times 635\times 10^{- 9}\times 3.53}{1.19\times 10^{- 3}} = 1.88\ mm$

Also, we know that the 1st dark fringe from the central fringe is given by:

$y = \frac{(n + \frac{1}{2})\lambda x}{d}$

$y = \frac{(1 + \frac{1}{2})\times 635\times 10^{- 9}\times 3.53}{1.19\times 10^{- 3}} = 2.83\ mm$