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Physics · 2026 · 3 marks
CBSE 2026 · Region 1 · Set 1 · Q28
(a) State the two conditions under which total internal reflection occurs. A transparent container contains layers of three immiscible transparent…
(a)
State the two conditions under which total internal reflection occurs.
A transparent container contains layers of three immiscible transparent liquids A, B and C of refractive indices n, $\displaystyle \frac{3}{4} \mathrm{n}$ and $\displaystyle \frac{2}{3} \mathrm{n}$, respectively. A laser beam is incident at the interface between A and $\displaystyle B$ at an angle $\displaystyle \theta$ as shown in figure. Prove that the beam does not enter region C at all for $\displaystyle \sin \theta \geq \frac{2}{3}$.
Marking-scheme solution
(a)(i)
Light must travel from denser medium to rarer medium.
(ii)
Angle of incidence must be greater than Critical angle.
$\displaystyle \mathrm{i}>i_{\mathrm{c}}$
(b)
For refraction at AB interface
$\displaystyle \dfrac{\sin \theta}{\sin \theta_{1}}=\dfrac{3 \mathrm{n} / 4}{\mathrm{n}}$
$\displaystyle \sin \theta=\dfrac{3}{4} \sin \theta_{1}$ ---------- ($\displaystyle 1$)
For refraction at BC interface
$\displaystyle \dfrac{\sin \theta_{1}}{\sin r}=\dfrac{2 \mathrm{n} / 3}{3 \mathrm{n} / 4}$
$\displaystyle \sin \theta_{1}=\dfrac{8}{9} \sin r$ ---------- ($\displaystyle 2$)
From equations ($\displaystyle 1$) and ($\displaystyle 2$)
$\displaystyle \dfrac{3}{2} \sin \theta=\sin r$
for $\displaystyle \sin \theta=\dfrac{2}{3}$
$\displaystyle \sin r=1$ i.e $\displaystyle r=90^{\circ}$
Ray grazes the surface
Hence for $\displaystyle \sin \theta \geq \dfrac{2}{3}$ does not enter the region C at all
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CBSE Class 12 Physics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.