Question

Coherent light with wavelength 601 nm passes through two very narrow slits, and the interference pattern is observed on a screen a distance of 3.00 m from the slits. The first-order bright fringe is a distance of 4.84 mm from the center of the central bright fringe. For what wavelength of light will thefirst-order dark fringe be observed at this same point on the screen?

Answer 1

The wavelength is
`\lambda = 1805 nm`

Step-by-step explanation:

From the question we are told that

The wavelength of the light is
`\lambda = 601 \ nm = 601 *10^(-9) \ m`

The distance of the screen is D = 3.0 m

The fringe width is
`y = 4.84 \ mm = 4.84 *10^(-3) \ m`

Generally the fringe width for a bright fringe is mathematically represented as

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

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

=>
`d = ( 601 *10^(-9) * 3)/( 4.84 *10^(-3 ))`

=>
`d = 0.000373 \ m`

Generally the fringe width for a dark fringe is mathematically represented as

`y_d = [m + (1)/(2) ] * (\lambda D )/(d )`

Here m = 0 for first order dark fringe

So

`y_d = [0 + (1)/(2) ] * (\lambda D )/(d )`

looking at which we see that
`y_d = y`

`4.84 *10^(-3) = [0 + (1)/(2) ] * (\lambda * 3 )/( 0.000373 )`

=>
`\lambda = 1805 *10^(-9) \ m`

=>
`\lambda = 1805 nm`