Question

A double slits separated by 0.0580 mm is located at a distance of 1.50 m from a screen. (a) If yellow light of wavelength 588 nm strikes the double slit, what is the separation between the first-order and third-order dark fringes on the screen

Answer 1

The separation between third order and first order is 0.0304 m

Step-by-step explanation:

Given:

Separation between two slit
`d = 0.0580 * 10^(-3)` m

Distance between slit and screen
`D = 1.50` m

Wavelength of light
`\lambda = 588 * 10^(-9)` m

From the formula of interference of light,

`d \sin \theta = n\lambda`

Here
`\sin \theta = (x)/(D)`

`(dx)/(D) = n \lambda`

`x = (n\lambda D)/(d)`

Where
`x =` separation between fringes

Here we have to find between third order and first order,

`x = ((n_(3) - n_(1))\lambda D )/(d)`

Where
`n_(3)` = 3
`n_(1)` = 1

`x = (2 * 588 * 10^(-9) * 1.50)/(0.0580 * 10^(-3) )`

`x = 0.0304` m

Therefore, the separation between third order and first order is 0.0304 m