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

Answer:

The  value is  $d = 0.000293 \ m$

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  

        $d sin \theta = n * \lambda$

=>     $d = \frac{n * \lambda}{sin \theta}$

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

      $sin (\theta) = \frac{y}{D}$

So  

          $d = \frac{n * \lambda}{\frac{y}{D} }$

=>       $d = \frac{10 * 633 *10^{-9}}{\frac{0.054}{ 2.5} }$

=>      $d = 0.000293 \ m$