Two small angled transparent prisms (each or refracting angle `A = 1^(@))` are so placed that their bases coincide, so that common base is BC. This device is called Fresnel's biprism and is used to obtain coherent sources of a point source S illuminated by monochromatic light of wavelength `6000 Å` placed at a distance `a = 20` cm. Calculate the separation between coherent sources. If a screen is placed at a distance `b = 80` cm. from the device, what ist the finge which of fringes obtained (Refractive index of material of each prism `= 1.5.)`

Explanation

The virtual images of slit S are formed at `S_(1)` and `S_(2)` by means of prism ABC and BCE, respectively. These images act as coherent sources. The deviation produced by small-angled prism is
`delta = (mu - 1) A`
Also `nu tan delta = delta (SS_(1))/(AS_(1)) = (d//2)/(a)`
Therefore, separation between coherent sources is
`d = 2a delta = 2a (mu - 1) A`
Hence, `a = 20 cm = 0.20 m`
` A = 1^(@) = (pi)/(180) = (3.14)/(180)` rad
`:. d = 2 xx 0.20 xx (1.5 - 1 ) (3.14)/(180) m = 3.84 xx 10^(-3) m`
Separaton between coherent sources and screen is
`D = a + b = 20 + 80 = 100 cm = 1 m`
`lambda = 6000 Å = 6000 xx 10^(-10) cm`
Therefore, fringe width
`beta = (D lambda)/(d) = (1 xx 6000 xx 10^(-10))/(3.48 xx 10^(-3))`
`= 1.724 xx 10^(-4)m = 0.1724 mm`
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