Question

Coherent light with wavelength 591 nm passes through two very narrow slits, and the interference pattern is observed on a screen a distance of 3.00 m from the slits. The first-order bright fringe is a distance of 4.84 mm from the center of the central bright fringe. For what wavelength of light will the first-order dark fringe be observed at this same point on the screen?

Answer 1

Answer:

The wavelength will be "1.182 μm".

Explanation:

The given values are:

Wavelength

$\lambda=591 \ nm$

or,

  $=591\times 10^-9 \ m$

Distance,

$d = 3.00 m$

$n = 1$

Distance of fringe from center,

$y = 4.84 \ mm$

We have to find the wavelength of first order dark fringe,

$\lambda = ?$

As we know,

⇒ $y_{bright} =\frac{1\times \lambda\times L}{d}$

On putting the given values in the formula, we get

   $0.00484=\frac{1\times (591\times 10^{-9})\times 3}{d}$          

On applying the cross multiplication, we get

   $\lambda = \frac{0.00484\times 000036632}{0.5\times 3}$

      $=1182\times 10^{-9}$

or,

      $=1.182 \ \mu m$