Question

Light from a helium-neon laser (λ = 633 nm) is used to illuminate two narrow slits. The interference pattern is observed on a screen 2.5 m behind the slits. Eleven bright fringes are seen, spanning a distance of 54 mm. What is the spacing (in mm) between the slits?

Answer 1

The value is
`d = 0.000293 \ m`

Step-by-step explanation:

From the question we are told that

The wavelength is
`\lambda = 633 \ nm = 633 *10^(-9) \ m`

The distance of the screen is
`D = 2.5 \ m`

The order of the bright fringes is
`n = 10` (10 fringe + central maximum = eleven bright fringes )

The distance between the fringe is
`y = 54 \ mm = 0.054 \ m`

Generally the condition for constructive interference is

`d sin \theta = n * \lambda`

=>
`d = (n * \lambda)/(sin \theta)`

Now from the SOHCAHTOA rule the angle
`sin \theta` is mathematically represented as

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

So

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

=>
`d = (10 * 633 *10^(-9))/((0.054)/( 2.5) )`

=>
`d = 0.000293 \ m`