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In a YDSE perfromed with light of wavel...

In a YDSE perfromed with light of wavelength `600 Å`, the screen is placed 1 m from the slits. Fringes formed on the screen are observed by a student sitting close to the slits. The student's eye can distinguish two neighboring fringes. If they subtend an angle more then 1 minute of ace, then
Find the location of third bright fringe from center of the screen.

A

`(3)/(pi)`mm

B

`(6)/(pi)mm`

C

`(4.5)/(pi)mm`

D

`(6.48)/(pi)mm`

Text Solution

Verified by Experts

The correct Answer is:
D
(i) Given `lamda=6000Å,D=1m`
We know that 1 minute`=(1)/(60^(@))`

Fringe width `=beta=(Dlamda)/(d)implies theta=beta//D=lamda//dimplies d=(lamda)/(theta)`
for maximum d, minimum value of `theta` has to be used
`theta_("min")=1` min for `are=(1)/(60)xx(pi)/(180)`radians
`implies d_(max)=(6000Å)/((1)/(60)xx(pi)/(180))=(180xx60xx6000Å)/(pi)`
`d_(max)=(6.48)/(pi)mm`.
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