Consider a Young's double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength such that the first minima occurs directly in front of the slit `(S_(1))` ?

Options

A. `(lambda)/(2(sqrt(5)-2))`
B. `(lambda)/((sqrt(5)-2))`
C. `(lambda)/(2(5-sqrt(2)))`
D. `(lambda)/(2(5-sqrt(2)))`

Answer

A

Explanation

Right angle,
In `S_(2)S_(1)Z_(1)S_(1),Z_(1)=r_(1) =2d`
`S_(2)Z_(1)=r_(2)=sqrt(4d^(2)+d^(2))=sqrt(5)d`
Path difference `(2n-1)(lambda)/(2)`
`r_(2)-r_(1)=(lambda)/(2) " " [ :.` For first minimum n=1]
`:. sqrt(5)d-2d=(lambda)/(2)`
`:.d[sqrt(5)-2]=(lambda)/(2)`
`:.d=(lambda)/(2(sqrt(5)-2))`