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Physics · 2022 · 3 marks
CBSE 2022 · Region 5 · Set 3 · Q10
A ray of light passes through a prism of refractive index √ 2 as shown in the figure. Find: (i) The angle of incidence (∠ r_2) at face AC. (ii) The…
A ray of light passes through a prism of refractive index $\displaystyle \sqrt{2}$ as shown in the figure. Find :
(i)
The angle of incidence $\displaystyle \left(\angle \mathrm{r}_{2}\right)$ at face AC.
(ii)
The angle of minimum deviation for this prism.
Marking-scheme solution
(i)
As the emergent ray grazes along the side AC, therefore
$$\frac{1}{\sqrt{2}}=\frac{\sin r_{$\displaystyle 2$}}{\sin $\displaystyle 90$^{$\displaystyle 0$}}
$$$$
\therefore r_{$\displaystyle 2$}=$\displaystyle 45$^{\circ}
$$(ii) $\displaystyle \mu=\frac{\sin \left(\dfrac{A+\boldsymbol{\delta} m}{2}\right)}{\sin \dfrac{A}{2}}$
$$\sqrt{2}=\frac{\sin \left(\dfrac{$\displaystyle 60$^{$\displaystyle 0$}+\boldsymbol{\delta} m}{$\displaystyle 2$}\right)}{\sin $\displaystyle 30$^{$\displaystyle 0$}}
$$$$
\therefore \delta_{\mathrm{m}}=$\displaystyle 30$^{$\displaystyle 0$}
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