In a Young's double slit experiment, light of wavelength 5900 Å is used. When the slits are 2 mm apart, the fringe width is 1.3mm. If the slit separation is increased to one and half times the previous value, then the fringe width will be

Options

A. `0.9 mm`
B. `0.8 mm`
C. `1.8 mm`
D. `1.6 mm`

Answer

B

Explanation

In a Young.s double slit experiment, wavelength of light, `lambda = 5900 Å` and distance between the slits, `d_(1) = d = 2 xx 10^(-3) m`,
Fringe width, `beta_(1) = 1.2 xx 10^(-3) m` and `d_(2) = (3)/(2)d`
As, the fringe width,
`beta = (lambda D)/(d)`
So, `beta_(1) = (lambda_(1) D_(1))/(d_(1))` and `beta_(2) = (lambda_(2)D_(2))/(d_(2))`
Putting the given values, we get
`rArr (1.2 xx 10^(-3))/(beta_(2)) = 0.8mm`
Hence, the correct option is (b).