For a ray of light, the critical angle is minimum, when it travels from
For a ray of light, the critical angle is minimum, when it travels from
glass to air
air to glass
glass to water
water to glass
Solution
The critical angle \(c\) for total internal reflection (TIR) when light travels from a medium of refractive index \(n_1\) to a medium of lower refractive index \(n_2\) is given by
\(\sin c=\frac{n_2}{n_1}\)
where \(n_1>n_2\).
The smaller the ratio \(\frac{n_2}{n_1}\), the smaller \(\sin c\), and hence the smaller the critical angle \(c\).
From the options, the valid scenarios for TIR are only those in which the first medium has a higher index than the second. That is:
\(\begin{aligned}
& \text { Glass to air }\left(n_{\text {glass }} \approx 1.5, n_{\text {air }} \approx 1.0\right) \\
& \sin c=\frac{1.0}{1.5}=\frac{2}{3} \quad \Longrightarrow \quad c \approx 42^{\circ}
\end{aligned}\)
Glass to water \(\left(n_{\text {glass }} \approx 1.5, n_{\text {water }} \approx 1.33\right)\)
\(\sin c=\frac{1.33}{1.5} \approx 0.887 \quad \Longrightarrow \quad c \approx 62^{\circ}\)
Clearly, the critical angle is smaller for glass-to-air than for glass-to-water.
Hence, the critical angle is minimum when light travels from glass to air.
Answer: (A) glass to air.