Question

In a thin prism of glass (refractive index $1.5$), which of the following relations between the angle of minimum deviation ${\delta }_m$ and angle of refraction $r$ will be correct ?

• A. ${\delta }_m=r$
• B. ${\delta }_m=1.5r$
• C. ${\delta }_m=2r$
• D. ${\delta }_m=\frac{r}{2}$

Answer 1

Answer: (A)

,For small angle prism, angle of minimum deviation is given by,

${\delta }_m=(\mu -1)A$

where ${\delta }_m$ is angle of minimum deviation,$\mu$ is refractive index, A is angle of prism

Also at angle of minimum deviation, A = 2r

$=(\mu -1)\left(2r\right)$

$=(1.5-1)\left(2r\right)$

$=0.5\times 2r=r$

Why this question? Tip: For thin prism (of small angle), formula for minimum deviation simplifies to: $\mu =\frac{\frac{A+{\delta }_m}{2}}{\frac{A}{2}}=\frac{A+{\delta }_m}{A}$