Question

Monochromatic light falls on two very narrow slits 0.047 mm apart. Successive fringes on a screen 6.60 m away are 8.9 cm apart near the center of the pattern.
Determine the wavelength and frequency of the light.

Answer 1

Answer::

   $\lambda = 634 nm$

  $f = 4.73 *10^{14} \ Hz$

Explanation:

From the question we are told that

      The  distance of separation is  $d = 0.047 \ mm = 0.047 *10^{-3} \ m$

       The  distance of the screen is  $D = 6.60 \ m$

      The  width of the fringe is $y = 8.9 \ cm = 0.089 \ m$

     

Generally the width of the width of the fringes is mathematically represented as

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

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

=>      $\lambda = \frac{ 0.089 * (0.047 *10^{-3}) }{6.60 }$

=>    $\lambda = 634 *10^{-9}$

=>  $\lambda = 634 nm$

Generally the speed of light is mathematically represented as

         $c = f * \lambda$

=>       $f= \frac{ c}{\lambda }$

=>         $f= \frac{ 3.0 *10^{8}}{634 *10^{-9}}$

=>     $f = 4.73 *10^{14} \ Hz$