In a double slit experiment utilizing light of wavelength , a plate of refractive index and thickness t is placed in front of one of the slits. Assuming no light absorption in the plate, what must be the minimum thickness t to render the intensity at the centre of the fringe pattern zero?

Step-by-step solution

When a transparent plate of thickness t and refractive index is placed in front of one of the slits, the additional path difference introduced at the centre of the screen is x = ( - 1)t . For the intensity at the centre of the fringe pattern to be zero, the path difference must satisfy the condition for destructive interference. The condition for a minimum is x = (2n - 1) 2 , where n = 1, 2, 3, For the minimum thickness t , we take n = 1 , which gives x = 2 . Equating the expressions for path difference, we get: (