Question

A diffraction pattern forms when light passes through a single slit. The wavelength of the light is 691 nm. Determine the angle that locates the first dark fringe when the width of the slit is (a) 3.8 × 10-4 m and (b) 3.8 × 10-6 m.

Answer 1

Step-by-step explanation:

Given that,

Wavelength of the light,
`\lambda=691\ nm=691* 10^(-9)\ m`

(a) Slit width,
`a=3.8* 10^(-4)\ m`

The angle that locates the first dark fringe is given by :

`sin\theta=(\lambda)/(a)`

`sin\theta=(691* 10^(-9))/(3.8* 10^(-4))`

`\theta=0.104^(\circ)`

(b) Slit width,
`a=3.8* 10^(-6)\ m`

The angle that locates the first dark fringe is given by :

`sin\theta=(\lambda)/(a)`

`sin\theta=(691* 10^(-9))/(3.8* 10^(-6))`

`\theta=10.47^(\circ)`

Hence, this is the required solution.