Question

In a fresnel's biprism experiment, the refracting angles of the prism were ${0.75}^o$ and the refracting index of the prism was $2$ . With the single slit $2.5$ cm from the biprism, and using light of wavelength $290nm$, fringes were formed on a screen $1m$ from the single slit . The fringe width is

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

Answer 1

The correct option is C 0.044 cm

$d=2a(\mu -1)A$ ......(1)
where
d: distance between coherent sources
A: Prism angle
a: separation between prism and two coherent sources
D: distance between the sources and screen
Fringe width $\beta =\frac{D\lambda }{d}$ ....(2)
From (1)
$d=2\times 2.5\times {10}^{-2}\times (2-1)\times (\frac{0.75}{360}\times 2\pi )=0.065\times {10}^{-2}$
From (2)
$\beta =\frac{1\times 290\times {10}^{-9}}{0.065\times {10}^{-2}}=4429\times {10}^{-7}=0.044cm$