MHTCET 15 May 2024 Shift 1 Paper

Concept:Critical angle exists only when light travels from a denser medium to a rarer medium, and its value depends on the refractive index ratio of the two media.Explanation:The critical angle $c$ is given by $\sin c = \frac{n_2}{n_1}$, where $n_1$ is the refractive index of the denser medium and $n_2$ is that of the rarer medium, with $n_1 > n_2$.A smaller ratio $\frac{n_2}{n_1}$ gives a smaller $\sin c$, and hence a smaller critical angle $c$.Among the given options, total internal reflection is possible only when light goes from glass to air or glass to water, because in these cases the first medium is denser than the second.For glass to air: $n_{\text{glass}} \approx 1.5$, $n_{\text{air}} \approx 1.0$.So, $\sin c = \frac{1.0}{1.5} = \frac{2}{3}$, which gives $c \approx 42^\circ$.For glass to water: $n_{\text{glass}} \approx 1.5$, $n_{\text{water}} \approx 1.33$.So, $\sin c = \frac{1.33}{1.5} \approx 0.887$, which gives $c \approx 62^\circ$.Since $42^\circ < 62^\circ$, the critical angle is clearly smaller for glass to air.Answer:(A) glass to air