Coherent light is incident normally on two identical slits X and Y. The diffracted light emerging from the slits superposes to produce an interference pattern on a screen positioned at a distance of 
from the slits. The figure below shows the arrangement and the central part of the interference pattern of bright and dark fringes formed on the screen.
The separation of the slits is 
. The distance between the centres of adjacent bright fringes is 
.
Calculate the wavelength 
of the light.
Light waves from slits X and Y in (a) arrive at a point between adjacent bright fringes on the screen. The figure below shows the variation of displacement with time for the waves arriving at the point where they meet.
A student makes two statements about the waves at this point:
Statement 1: ‘The phase difference between the waves is 
.’
Statement 2: ‘The amplitude of the resultant wave is zero.’
Explain how statement 1 is correct.
State and explain whether statement 2 is correct.
The width of each slit in (a) is decreased by the same amount. There is no change to the separation of the slits. Describe and explain the effect, if any, of this change on the appearance of the interference pattern.
.
