Question

Light from a laser (lambda= 406.192 nm) is used to illuminate two narrow slits. The interference pattern is observed on a screen 5.937 m behind the slits. 24 bright fringes are seen, spanning a distance of 39.835 mm (they are not necessarily centered, you don't know where the center is, this is not important here). What is the spacing (in mm) between the slits? Give the numerical answer only, in m

Answer 1

Answer:

The spacing between the slits is    $d = 0.00145m$                

Explanation:

From the question we are told that

  The wavelength of the light is $\lambda = 406.192nm = 406.192*10^{-9} m$

   The distance of the slit from the screen is $D = 5.937 \ m$

    The number of bright fringe is $n = 24$

     The  length the fringes span is   $L = 39.835 mm = \frac{39.835 }{1000} = 0.0398 m$

The fringe width (i.e the distance of between two successive bright or dark fringe) is mathematically represented as

             $\beta = \frac{\lambda D}{d}$

Where d is  the distance between the  slits

            $\beta$ is the fringe width which can also be evaluated as

                         $\beta = \frac{L}{n}$

Substituting values

                        $\beta = \frac{0.0398}{24}$

                          $\beta = 1.660 *10^{-3}$

Making d the subject of formula in the above equation

                $d = \frac{\lambda D}{\beta }$

Substituting values

                $d = \frac{406.192 *10^{-9} * 5.937 }{1.660 *10^{-3}}$

                    $d = 0.00145m$