CBSE 2026 · Region 4 · Set 2 · Q32 · 5 marks
(i)Define refractive index of a medium in terms of speed of light.(ii)Derive the relation for the refractive index ( $\displaystyle \mu$ ) of a prism in terms of angle of minimum derivation $\displaystyle \left(\delta_{\mathrm{m}}\right)$ and angle of prism (A).(iii)A ray of light QP is incident normally on the face BC of a triangular prism ABC of refractive index $\displaystyle 1.5$ kept in air, as shown in the figure. Trace the path of the ray as it passes through the prism and give relevant explanation.
(i)What is the difference between a ray and a wavefront ?(ii)A plane wave is incident on a reflecting surface. Using Huygens principle, show how it is reflected from the surface. Hence, verify the law of reflection.(iii)Depict refraction of a plane wave by a convex lens.
(i)
Define refractive index of a medium in terms of speed of light.
(ii)
Derive the relation for the refractive index ( $\displaystyle \mu$ ) of a prism in terms of angle of minimum derivation $\displaystyle \left(\delta_{\mathrm{m}}\right)$ and angle of prism (A).
(iii)
A ray of light QP is incident normally on the face BC of a triangular prism ABC of refractive index $\displaystyle 1.5$ kept in air, as shown in the figure. Trace the path of the ray as it passes through the prism and give relevant explanation.
(i)
What is the difference between a ray and a wavefront ?
(ii)
A plane wave is incident on a reflecting surface. Using Huygens principle, show how it is reflected from the surface. Hence, verify the law of reflection.
(iii)
Depict refraction of a plane wave by a convex lens.
Marking-scheme solution
(i)
Refractive index of a medium is the ratio of the speed of light in vacuum to the speed of light in the medium. (Alternatively: $\displaystyle \mathrm{n}_{21}=\dfrac{\mathrm{c}}{\mathrm{v}}$)
(ii)
In the quadrilateral AQNR, two of the angles (at the vertices Q and R) are right angles, therefore the sum of the other angles of the quadrilateral is $\displaystyle 180^{\circ}$: $\displaystyle \angle \mathrm{A}+\angle \mathrm{QNR}=180^{\circ}$
From the triangle QNR, $\displaystyle r_{1}+r_{2}+\angle \mathrm{QNR}=180^{\circ}$. Comparing these two equations: $\displaystyle r_{1}+r_{2}=\mathrm{A} \quad \ldots(1)$
The total deviation $\displaystyle \delta$ is the sum of the deviations at the two faces: $\displaystyle \delta=\mathrm{i}+\mathrm{e}-\mathrm{A} \quad \ldots(2)$
For $\displaystyle \delta=\delta_{m}$, $\displaystyle \mathrm{i}=\mathrm{e}$, which implies $\displaystyle r_{1}=r_{2}$. From ($\displaystyle 1$) and ($\displaystyle 2$): $\displaystyle r=\dfrac{\mathrm{A}}{2}$, $\displaystyle \mathrm{i}=\dfrac{\mathrm{A}+\delta_{m}}{2}$
Refractive index of the prism: $\displaystyle n_{21}=\dfrac{n_{2}}{n_{1}}=\dfrac{\sin \dfrac{\left(\mathrm{A}+\delta_{m}\right)}{2}}{\sin \dfrac{\mathrm{A}}{2}}$
(iii)
The ray QP strikes the face BC normally and hence goes undeviated. As $\displaystyle \mathrm{i}>\mathrm{i}_{\mathrm{c}}$, it undergoes TIR. It strikes the face AC normally and comes out undeviated.
(i)
Ray — it is a straight line depicting the rectilinear propagation of light.
Wavefront — it is the locus of points which oscillate in the same phase.
(ii)
If $\displaystyle v$ represents the speed of the wave in the medium and $\displaystyle \tau$ represents the time taken by the wavefront to advance from the point B to C, then the distance $\displaystyle \mathrm{BC}=v \tau$
Let CE represent the tangent plane drawn from the point C to this sphere. Then $\displaystyle \mathrm{AE}=\mathrm{BC}=v \tau$
Considering the triangles EAC and BAC, they are congruent. Therefore the angles i and r would be equal.
(iii)
An incident plane wave, on passing through a convex lens, emerges as a spherical wavefront of radius $\displaystyle f$ converging towards the focus.
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CBSE Class 12 Physics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.