Question

In a fresnel's bi-prism experiment , the refracting angles of the prism were 2.5${}^o$ and the refracting index of the glass was 1.5 . With the single slit 10 cm from the bi-prism ,fringes were formed on a screen 1 m from the single slit . The fringe width is 0.1375 mm . The wavelength of light is

• A. 600 nm
• B. 1200 nm
• C. 60 A${}^o$
• D. 120 A${}^o$

Answer 1

The correct option is A 600 nm

For a fresnel biprism having an angle of $\alpha$ and refractive index $\mu$, frindge width $\beta =\frac{\lambda D}{2a(\mu -1)\alpha }$

Given,
$\beta =0.1375mm,\alpha =2.5=\frac{2.5\times \pi }{180}rad,D=1000mm,a=100mm\&\mu =1.5$
$\therefore 0.1375=\frac{\lambda \left(mm\right)\times 1000}{2\times 100\times (1.5-1)\times \left(\frac{2.5\times \pi }{180}\right)}$
$\Rightarrow \lambda =6\times {10}^{-4}mm=600nm=6000\mathring{A}$