Question

In the two-slit experiment, monochromatic light of wavelength 600 nm passes through a 19) pair of slits separated by 2.20 x 10-5 m. (a) What is the angle corresponding to the first bright fringe? (b) What is the angle corresponding to the second dark fringe?

Answer 1

Step-by-step explanation:

It is given that,

Wavelength of monochromatic light,
`\lambda=600\ nm=6* 10^(-7)\ m`

Slits separation,
`d=2.2* 10^(-5)\ m`

(a) We need to find the angle corresponding to the first bright fringe. For bright fringe the equation is given as :

`d\ sin\theta=n\lambda`, n = 1

`\theta=sin^(-1)((\lambda)/(d))`

`\theta=sin^(-1)((6* 10^(-7))/(2.2* 10^(-5)))`

`\theta=1.56^(\circ)`

(b) We need to find the angle corresponding to the second dark fringe, n = 1

So,
`d\ sin\theta=(n+(1)/(2))\lambda`

`sin\theta=(3\lambda)/(2d)`

`\theta=sin^(-1)((3\lambda)/(2d))`

`\theta=sin^(-1)((3* 6* 10^(-7))/(2* 2.2* 10^(-5)))`

`\theta=2.34^(\circ)`

Hence, this is the required solution.