Question

Describe biprism experiment to find the wavelength of monochromatic light. Draw the necessary ray diagram from magnified and diminished images of virtual sources.

Answer 1

A Fresnel Biprism is a variation on the Young’s Slits experiment. The Fresnel biprism consists of two thin prisms joint at their bases to form an isosceles triangle. A single wavefront impinges on both prisms; the left portion of the wavefront is refracted right while the right segment is refracted left. In the region of superposition, interference occurs as here two virtual sources exist.

Here $d$ is determined by placing a converging lens between the biprism and the screen and forming real images of the virtual slits on the screen. From the magnification formula,

$\frac{d_1}{d}=\frac{v_1}{u_1}and\frac{d_2}{d}=\frac{v_2}{u_2}=\frac{u_1}{v_1},$

We find that $d=\sqrt{d_1{d}_2}$

Putting this into the Young’s Slits equation gives $\lambda =S\frac{\sqrt{d_1{d}_2}}{L}$

Given $v_{\omega }-v_g=2.7\times {10}^{7}m/s,{\mu }_g=1.5,{\mu }_{\omega }=1.33$
$\because v_{\omega }=\frac{C}{{\mu }_{\omega }}=\frac{C}{1.333}$
$\because v_g=\frac{C}{{\mu }_g}=\frac{C}{1.5}$ $\therefore v_{\omega }-v_g=\frac{C}{{\mu }_{\omega }}-\frac{C}{{\mu }_g}$
$=C[\frac{1}{1.333}-\frac{1}{1.5}]$
$\Rightarrow 2.7\times {10}^7=C\left[\frac{1.5-1.333}{1.5\times 1.333}\right]$
$\Rightarrow C=323272455.1=3.23\times {10}^{8}m/s$