Question

Two small angled transparent prisms (each of refracting angle $A=1^{\circ }$) 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 $6000\stackrel{\circ }{A}$ placed at a distance $a=20\text{cm}$. Calculate the separation between coherent sources. If a screen is placed at a distance $b=80$\text{cm}\) from the device, what is the fringe width of fringes (in cm) obtained
(Refractive index of material of each prism = 1.5).

Answer 1

for upper prism:

In $\Delta OS{S}_1$
$tan\delta =\frac{d}{2}$
because it's a thin prism then,
$tan\delta =\frac{d}{2\times 20}=\frac{d}{40}$

$tan\delta =\delta$ (for a thin prism)
$\delta =(\mu -1)A$
Given, $\mu =1.5,A=1^o$
$\frac{d}{40}=(1.5-1)\times \frac{3.15}{180}d=40(1.5-1)\times \frac{3.15}{180}d\approx \frac{1}{3}=0.34cm$