Question

What is the wave length if the distance from the central bright region to the sixth dark fringe is 1.9 cm . Answer in units of nm.

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

The wavelength is
`\lambda = 622 nm`

Step-by-step explanation:

From the question we are told that

The distance of the slit to the screen is
`D = 5 \ m`

The order of the fringe is m = 6

The distance between the slit is
`d = 0.9 \ mm = 0.9 *10^(-3) \ m`

The fringe distance is
`Y = 1.9 \ cm = 0.019 \ m`

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

`Y = ([2m - 1 ] * \lambda * D )/(2d)`

=>
`\lambda = (Y * 2 * d )/([2*m - 1] * D)`

substituting values

=>
`\lambda = (0.019 * 2 * 0.9*10^(-3) )/([2*6 - 1] * 5)`

=>
`\lambda = 6.22 *10^(-7) \ m`

`\lambda = 622 nm`