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In Young's double slit experiment the tw...

In Young's double slit experiment the two slits are d distance apart. Interference pattern is observed on a screen at a distance D from the slits. A dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light is

A

`(D^(2))/(2d)`

B

`(d^(2))/(2D)`

C

`(D^(2))/(d)`

D

`(d^(2))/(D)`

Text Solution

Verified by Experts

The correct Answer is:
D

From figure, `S_(1)P=D`
`S_(2)P=(D^(2)+d^(2))^(1//2)=D(1+(d^(2))/(D))^(1//2)`
`=D(1+(1)/(2)(d^(2))/(D^(2)))=D+(d^(2))/(2D)`
Path difference, `Deltax=S_(2)P-S_(1)P=D+(d^(2))/(2D)-D=(d^(2))/(2D)`
For dark fringe, `(d^(2))/(2D)=(lamda)/(2) or lamda=(d^(2))/(D)`.
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