Question

In measuring the width of a hair sample, a light of wavelength 500 nm is used. The hair sample is 40 um in radius. With the screen 6 meters away from the hair sample, where would the second dark band away from the central bright spot be located?

Answer 1

The distance of the second dark band away from the central bright spot be located is
`5.625*10^(-2)\ m`

Step-by-step explanation:

Given that,

Wave length = 500 nm

Radius
`d= 40\ \mu m`

Distance from the hair sample D= 6 m

We need to calculate the distance of the second dark band away from the central bright spot be located

`\sin\theta=(y)/(D)`

`\sin\theta=(y)/(6)`

Using formula for dark fringe

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

Put the value into the formula

`(2-(1)/(2))*500*10^(-9)=2*40*10^(-6)*(y)/(6)`

`y=((2-(1)/(2))*500*10^(-9)*6)/(2*40*10^(-6))`

`y=0.05625\ m`

`y=5.625*10^(-2)\ m`

Hence, The distance of the second dark band away from the central bright spot be located is
`5.625*10^(-2)\ m`