A coherent parallel beam of light of wavelength `5000 A` is incident normally on the plane of slits. The slit `S_(1)` is covered with a slab of refractive index `mu_(s) = 1.5` and thickness `t = 4 xx 10^(-5)m` as shown. The separation between the slits is `d = 1 mm` and the separtion between the plane of slits and screen is `D = 1m`. Then the position of the central maxima formed on the screen is

Options

A. `1 cm` above point 'O'.
B. `2 cm` above point 'O'.
C. `1 cm` below point 'O'.
D. `2 cm` below point 'O'.

Answer

B

Explanation

For central maxima `d sin theta = (mu_(s) - 1) t`
`1 xx 10^(-3) sin theta = (1.5 -1) xx 10^(-5)`
`1 xx 10^(-3) sin theta = 2 xx 10^(-5)`
`sin theta = (1)/(50)`
`tan theta = (1)/(50)` ("for small `'theta'`)
`(y)/(D) = (1)/(50)`
` :. y = (D)/(50) = (100)/(5) cm = 2 cm` (above point 'O' )