obtain the expression for Fringe width of a bright fringe obtained in a interference experiment of Young.

if in youngs SINGLE slits experiment let the gap betwwen slits is ‘a’ then the distance between screen and slit is say R and draw a line exactly to the center of bright fring and consider a bright fring which is at a distance of y_m and draw a line from the slit so we get a triangle 

as we know brigh fring is due to constructive interference so from path diference we get

Dsin(∂)=lamda×m

sin∂=lamda×m÷a

from our triangle ;tan∂=y_m÷R

AS ∂ IS VERY SMALL sin∂~tan∂

lamda×m÷d=y_m÷R

y_m=lamda×m×R÷a

assume for a bright at a distance of y_m+1

we get y_m+1=(m+1)lamda×R÷d

by subtracting y_m+1-y_m=lamda×R÷a