A light of wavelength `6000 Å` shines on two narrow slits separeted by a distance 1.0 mm and illuminates a screen at a distance 1.5 m away. When one slit is covered by a thin glass plate of refractive index 1.8 and other slit by a thin glass plate of refractive index `mu`, the central maxima shifts by 0.1 rad. Both plates have the same thickness of 0.5 mm. The value of refractive index `mu` of the glass is

Options

A. 1.4
B. 1.5
C. 1.6
D. none of these

Answer

c

Explanation

Changed in path difference for any point on screen is `|mu - 1.8|t`.
For central maxima, phase difference `= 0`.
Hence,
`d sin theta - |mu - 1.8|t = 0`
`implies d theta = |mu - 1.8|t` [`theta` is very small and is in radium]
`implies |mu - 1.8| = (10^(3) xx 0.1)/(0.5 xx 10^(-3)) = 0.2`
`mu = 2` or `1.6`.