In a biprism expeirment the distance between the thrid and thirteenth dark fringes on the same side of central bright fringe is y when light of wavelenght 5400Å is used. On replacing the source by another of a differnet wavleneght, without distrubing the adjustment of the appartus it is found tht the distance between the fourth and thirteenth dark fringes on the same side of the central bright fringe is the same as y. The wavelenght of ligh used in the second case is

Options

A. 3000Å
B. 4000Å
C. 5000Å
D. 6000Å

Answer

D

Explanation

`x_(13d)-x_(3d)=x'_(13d)-x'_(4d)`
`:.12.5beta_(1)-2.5beta_(1)=12.5beta_(2)-3.5beta_(2)`
`10beta_(1)=9beta_(2):.10lamda_(1)=9lamda_(2)`
`:.lamda_(2)=(10xx5400)/(9)=6000Å`