Question

In the Fresnel bi-prism experiment, the refractive index for the bi-prism is $\mu =3/2$ and fringe width obtained is $0.4mm$. If the whole apparatus is immersed as such in water then the fringe width will become(refractive index of water is $4/3$).

• A. $0.3mm$
• B. $0.225mm$
• C. $0.4mm$
• D. $1.2mm$

Answer 1

The correct option is D $1.2mm$

In a fresnel bi-prism, fringe width,${\omega }_{medium}=\frac{D{\lambda }_{medium}}{d_{medium}}$

where ${\lambda }_{medium}=\frac{{\lambda }_{vacuum}}{{\mu }_{medium}}$

and $d_{medium}\propto A(\frac{{\mu }_{bi-prism}}{{\mu }_{medium}}-1)$

Here ${\mu }_{medium}=\frac{4}{3}$ and ${\mu }_{bi-prism}=\frac{3}{2}$

Hence $\frac{{\omega }_{water}}{{\omega }_{vacuum}}=3$

Hence, ${\omega }_{water}=1.2mm$