Figure shows a modified Fresnel biprism experiment with monochromatic source of wavelength 500 nm. The refracting angle of glass prism is `2^(@)`. Find the fringe width.

Answer

0.1125 mm

Explanation

Angle of deviation of the prism with water on one side,
`delta = A [(mu_(g))/(mu_(m)) - 1] = (2)/(180) xx (22)/(7) [(3//2)/(4//3) - 1]`
`implies delta = (2 xx 11)/(90 xx 7) [(3)/(2) xx (3)/(4) - 1] = (2 xx 11 )/(90 xx 7) xx [(1)/(8)] = (11)/(90 xx 4 xx 7)`
`d = 2 delta l = (2 xx 11 xx 57.5)/(90 xx 4 xx 7) = (11 xx 115)/(90 xx 4 xx 7)`
`D = 1 + L = 150 cm`
Fringe width,
`beta = (11 xx 23)/(18 xx 4 xx 7) cm`
`0.1125 mm`