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Physics · 2026 · 3 marks
CBSE 2026 · Region 3 · Set 3 · Q23
A ray of light is incident at angle of 45° on one face of a prism with an equilateral triangular base. If it passes symmetrically through the prism,…
A ray of light is incident at angle of $\displaystyle 45$° on one face of a prism with an equilateral triangular base. If it passes symmetrically through the prism, find the :
(a)
angle of minimum deviation for the prism, and
(b)
refractive index of the material of the prism.
Marking-scheme solution
(a)
As the ray of light passes symmetrically through the prism, $\displaystyle \angle \mathrm{r}_{1}=\angle \mathrm{r}_{2}=\mathrm{r}$ and $\displaystyle \mathrm{i}=\mathrm{e}$
$\displaystyle \delta_{m}=2 \mathrm{i}-\mathrm{A}=2 \times 45^{\circ}-60^{\circ}=30^{\circ}$
(b)
$\displaystyle \mathrm{r}=\dfrac{\mathrm{A}}{2}=30^{\circ}$
$\displaystyle \mu=\dfrac{\sin \left(\dfrac{\mathrm{A}+\delta_{m}}{2}\right)}{\sin \dfrac{\mathrm{A}}{2}}=\dfrac{\sin \left(\dfrac{60^{\circ}+30^{\circ}}{2}\right)}{\sin 30^{\circ}}$
$\displaystyle =\dfrac{\sin 45^{\circ}}{\sin 30^{\circ}}=\sqrt{2}$
Alternatively:
$\displaystyle \mu_{\mathrm{a}} \sin \mathrm{i}=\mu_{\mathrm{g}} \sin \mathrm{r}$
$\displaystyle 1 \times \sin 45^{\circ}=\mu_{\mathrm{g}} \times \sin 30^{\circ}$
$\displaystyle \mu_{\mathrm{g}}=\sqrt{2}$
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