Question

A double-slit experiment is set up using red light (λ = 734 nm). A first-order bright fringe is seen at a given location on a screen.

What wavelength of visible light (between 380 nm and 750 nm) would produce a dark fringe at the identical location on the screen?

Answer 1

The wavelength of visible light = 489.33 nm

Step-by-step explanation:

In an
`m^(th)` order bright fringe;

`y_m = m ( \lambda R)/(d)`

For first order ; m = 1

∴
`y_1 = (\lambda R)/(d)`

For
`m^(th)` order dark fringe ;

`y_m = (m+ (1)/(2)) (\lambda R)/(d)`

first order
`y_1 = (1+ (1)/(2)) (\lambda R)/(d)`

`y_1 = ((3)/(2)) (\lambda R)/(d)`

Assuming the wavelength of second light is
`\lambda'`

Thus:

`\phi \ y_1 = (3)/(2) (\lambda' R)/(d)`

Given that :
`(y_1) bright =(b_1)dark`

`(\lambda R)/(d)= (3)/(2)(\lambda' R)/(d)`

`\lambda' = (2)/(3) \lambda`

`\lambda' = (2)/(3) *734`

`\lambda' =489.33 \ nm`