A monochromatic light source S of wavelength 440 nm is placed slightly above a plane mirror M as shown . Image of S in M can be used as a virtual source to produce interference fringes on the screen. The distance of source S from O is 20.0 cm, and the distance of screen from O is `100.0` cm (figure is not to scale). If the angle `theta = 0.50 xx10^(-3)` radians, the width of the interference fringes observed on the screen is –

Options

A. `2.20` mm
B. 2.64 mm
C. `1.10` mm
D. `0.55` mm

Answer

B

Explanation

Here D = (100 + 20 cos `theta`) d = 40 sin `theta , lambda` = 440 nm
`beta = (lambda D)/(d) = (440 xx 10^(-6) xx 120 xx 10^(2))/(2 xx 10^(-2) xx 10^(2) ) = 264 xx 10^(-2)`
`rArr 2.64` mm.