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

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* 10^(- 3)\ m`

Distance from the screen, x = 3.53 m

Wavelength of the light,
`\lambda = 635\ nm = 635* 10^(- 9)\ m`

Now,

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

`y = (n\lambda x)/(d)`

where

n = 1

`y = (1* 635* 10^(- 9)* 3.53)/(1.19* 10^(- 3)) = 1.88\ mm`

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

`y = ((n + (1)/(2))\lambda x)/(d)`

`y = ((1 + (1)/(2))* 635* 10^(- 9)* 3.53)/(1.19* 10^(- 3)) = 2.83\ mm`