In a Young's double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle `(1)/(40)` rad by using light of wavelength `lamda_(1).` When the light of wavelength `lamda_(2)` is used a bright fringe is seen at the same at the same angle in the same set up. Given that `lamda_(1) and lamda_(2)` are in visible range (380 nm to 740 nm), their values are :

Options

A. 380 nm, 525 nm
B. 625 nm, 500 nm
C. 400 nm, 500 nm
D. 380 nm, 500 nm

Answer

B

Explanation

`theta=y/D`
`1/40=(n_(1)lamda_(1)D/d)/D`
`1/40=(n_(1)lamda_(1))d=(n_(1)lamda_(1))/(0.1xx10^(-3))rArrn_(1)lamda_(1)=(10^(-4))/40=100000/40` nm
`=2500nm`
`lamda=2500/n`
`n=1tolamda=2500`
`n=2tolamda=1250`
`n=3tolamda~~800`
`n=4tolamda=625`
`n=5tolamda=500`
Ans. `lamda=500,625`