Question

In a Fresnel's biprism experiment , the refracting angles of the prism were 1.5${}^o$ and the refracting index of the glass was 1.5 . With the single slit 5 cm from the biprism, and using light of wavelength 580 nm, fringes were formed on a screen 1 m from the single slit . The fringe width is

• A. $0.44cm$
• B. $4.4cm$
• C. $0.044cm$
• D. $0.0044cm$

Answer 1

The correct option is C $0.044cm$

Separation between the coherent sources $d=2a(\mu -1)A$
where $a=$distance between the single slit and the biprism, A is the prism angle and $\mu$ is the refractive index of biprism.
$d=2\times 5\times (1.5-1)\times \left(\frac{1.5\times \pi }{180}\right)=10\times 0.5\times \left(\frac{1.5\times \frac{22}{7}}{180}\right)=0.13cm=0.13\times {10}^{-2}m$
Fringe width $\beta =\frac{D\lambda }{d}=\frac{1\times 580\times {10}^{-9}}{0.13\times {10}^{-2}}=4461.5\times {10}^{-7}m=0.0446cm$