Question

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

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

Answer 1

The correct option is A ${\delta }_m=r$

For a thin prism, angle of minimum deviation is given by :
${\delta }_m=(\mu -1)A$ ... (i)
Here,
$\mu =$ refractive index of prism
$A=$ angle of prism

For $\delta ={\delta }_m,i=e$ and $r_1=r_2=r$
$\Rightarrow r_1+r_2=A$
or, $2r=A$ ... (ii)

From (i) & (ii),
${\delta }_m=(\mu -1)2r$
$\Rightarrow {\delta }_m=(1.5-1)2r$
or, ${\delta }_m=(0.5\times 2)r$
$\therefore {\delta }_m=r$