Question

Light of wavelength 476.1 nm falls on two slits spaced 0.29 mm apart. What is the required distance from the slits to the screen if the spacing between the first and second dark fringes is to be 4.2 mm?

Answer 1

The distance is
`D = 2.6 \ m`

Step-by-step explanation:

From the question we are told that

The wavelength of the light is
`\lambda = 476.1 \ nm = 476.1 *10^(-9) \ m`

The distance between the slit is
`d = 0.29 \ mm = 0.29 *10^(-3) \ m`

The between the first and second dark fringes is
`y = 4.2 \ mm = 4.2 *10^(-3) \ m`

Generally fringe width is mathematically represented as

`y = (\lambda * D )/(d)`

Where D is the distance of the slit to the screen

Hence

`D = (y * d)/(\lambda )`

substituting values

`D = ( 4.2 *10^(-3) * 0.29 *10^(-3))/( 476.1 *10^(-9) )`

`D = 2.6 \ m`