Question

A thin prism of glass is placed in air and water successively. If ${}_a{\mu }_g=3/2$ and ${}_a{\mu }_w=4/3$, then the ratio of deviations produced by the prism for a small angle of incidence when placed in air and water is:

• A. $9:8$
• B. $4:3$
• C. $3:4$
• D. $4:1$

Answer 1

Answer: (D)

$4:1$

Deviation from thin prism -

$\delta =(\mu -1)A$

- wherein

Applicable when A is very small

( i.e. thin prism )

$\delta =(\mu -1)A$ (for thin prism)

in air , ${\delta }_A=(\frac{3}{2}-1)A=\frac{A}{2}----------------------\left(1\right)$

in water ${\delta }_w=(=\frac{{\mu }_g}{{\mu }_w}-1)A$

$=(\frac{3}{\frac{2.4}{3}}-1)A$

${\delta }_w=\frac{A}{8}$

$\therefore \frac{{\delta }_a}{{\delta }_w}=4:1$