In a double slit experiment, the distance between the slits is increased 10 times wheares their distance from the screen is halved, then what is the new fringes width if the original fringe width is X?

Options

A. Becomes `X/(20)`
B. Becomes `(X)/(10)`
C. Becomes `(X)/(90)`
D. It remains same

Answer

A

Explanation

`X=(lamdaD)/(d)`
`D_(2)=(D_(1))/(2)` and `d_(2)=10d_(1)`
`therefore (X_(2))/(X_(1))=(D_(2))/(d_(1))xx(d_(1))/(D_(1))=(D_(1))/(2D_(1))xx(d_(1))/(10d_(1))=(1)/(20)`
`therefore X_(2)=(X_(1))/(20) or X_(2)=(X)/(20)`
thus the fringe width becomes `X/(20)`.