Question

Light passes through a 0.15 mm-wide slit and forms a diffraction pattern on a screen 1.25 m behind the slit. The width of the central maximum is 0.75 cm. What is the wavelength of the light

Answer 1

Answer:

The value is  $\lambda = 900 \ nm$

Explanation:

From the question we are told that

   The width of the slit is  $a = 0.15 \ mm = 0.00015 \ m$

     The distance of the screen from the slit is D = 1.25 m

      The width of the central maximum is $y = 0.75 \ cm = 0.0075 \ m$

Generally the width of the central maximum is mathematically represented as

         $y = \frac{m * D * \lambda}{a}$

Here  m is the order of the fringe and given that we are considering the central maximum, the order will be  m =  1  because the with of the central maximum separate's the and first maxima

So

        $\lambda = \frac{a y}{ m * D }$

=>     $\lambda = \frac{ 0.000015 * 0.0075}{ 1 * 1.2 }$

=>     $\lambda = 900 *10^{-9} \ m$

=>      $\lambda = 900 \ nm$