CBSE 2025 · Region 6 · Set 3 · Q21 · 2 marks
A tank is filled with a liquid of refractive index $\displaystyle \sqrt{2}$, up to a height of $\displaystyle 30$ cm . A tiny bulb is glowing at the bottom of the tank. Calculate the diameter of an opaque disc floating symmetrically on the liquid surface that can cut off completely the light from the bulb that comes out of the liquid surface.
Marking-scheme solution
$\displaystyle \sin i_c = \dfrac{1}{\sqrt{2}}$$\displaystyle i_c = 45^{0}$$\displaystyle \tan i_c = \dfrac{r}{d}$$\displaystyle r = d \tan 45^{0}$$\displaystyle r = 30 \times 1 \ \text{cm}$$\displaystyle D = 2r = 60 \ \text{cm}$Alternatively:$\displaystyle D = 2r = \dfrac{2d}{\sqrt{n^{2}-1}}$$\displaystyle = \dfrac{2 \times 30}{\sqrt{\left(\sqrt{2}\right)^{2}-1}}$$\displaystyle D = 60\,\text{cm}$Ray Optics and Optical InstrumentsTotal Internal ReflectionApplyvery_short_answermedium
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CBSE Class 12 Physics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.