Consider the arrangement shown in figure. The distance D is large compared to the searated d between the slits. a. Find the minimum value of d so that there is a dark fringe at O. b. Suppose d has this value. Find the distance x at which the next bright firnnge is formed. c.Find teh fringe width.

Answer

A, B, C, D

Explanation

From the diagram it can be seen that at point O,
Path differene `=(AB+BO)-(AC+CO)`
`=2(AB-AC)`
[Since AB=BO and AC=CO]`
`=2(sqrt(D^2+d^2D))`
For dark fringe path difference should be odd multiple of `lamda/2`
`So, 2(sqrt(D^2+d^2-D))=(2n+1)lamda/2`
`rarrsqrtD^2+d^2=D+(2n+1)lamda/4`
`rarr D^2+d^2=D^2+(2n+1)^2lamda^2/16+(2n+1)(lamdaD)/2`
Neglecting `(2n+1)^2lamda^2/16` as it is very small we get `d=(sqrt2n+1)(lamdaD)/2`
for minimum d putting n=0
`rarr d_(min)=sqrt(((lamdaD)/2))`