Question

Light of wavelength 520 nm is used to illuminate normally two glass plates 21.1 cm in length that touch at one end and are separated at the other by a wire of radius 0.028 mm. How many bright fringes appear along the total length of the plates.

Answer 1

Answer:

The number is  $Z = 216 \ fringes$

Explanation:

From the question we are told that

      The wavelength is  $\lambda = 520 \ nm = 520 *10^{-9} \ m$

       The length of the glass plates is $y = 21.1cm = 0.211 \ m$

      The distance between the plates (radius of wire ) =  $d = 0.028 mm = 2.8 *10^{-5} \ m$

   Generally the condition for constructive  interference in a film is mathematically represented as

            $2 * t = [m + \frac{1}{2} ]\lambda$

Where  t is the thickness of the separation between the glass i.e  

    t  = 0 at the edge where the glasses are touching each other and  

     t =  2d at the edge where the glasses are separated by the wire  

   m is the order of the fringe it starts from  0, 1 , 2 ...

So  

       $2 * 2 * d = [m + \frac{1}{2} ] 520 *10^{-9}$

=>   $2 * 2 * (2.8 *10^{-5}) = [m + \frac{1}{2} ] 520 *10^{-9}$

=>    

       $m = 215$

given that we start counting m from zero

   it means that the number of  bright fringes that would appear is

         $Z = m + 1$

=>    $Z = 215 +1$

=>     $Z = 216 \ fringes$