Question

in a double slit experiment to find the separation between slits by displacement method, the separation of images of slits were found to be 16 mm and 9mm respectively.the actual separation between slits will be
(a) 12.5 mm
(b) 12 mm
(c) 3.5 mm
(d) 144 mm

Answer 1

Answer is :  √(16 * 9) = 12 mm.

Formula :   d = √(d1 * d2) 

    d = actual separation between the two slits S1 and S2.
   d1 = separation between the two bright and enlarged 
          images of the slits when a Convex lens is kept 
          closer to the slits & images are focussed well.

   d2: separation between images when the convex lens 
         is moved towards the screen and diminished small 
         & focussed images of slits are formed on the screen.

Derivation:

     Magnification of the lens = m = is same in both positions
     of the lens.
         So m = d1/d  in the first  = d/d2 in the second
        =>   d1 d2 = d²    
        =>   d = √(d1 * d2)

      The displacement method means a convex lens is used to record the focussed enlarged images and then is displaced to find diminished images. In both cases the image height is measured. Then the actual height of the object is calculated.

     Same method and formula is used even in displacement method with the Fresnel Biprism experiment with one real light source. There will be two virtual light sources from the biprism. The separation between them is found using the above formula.