MHT CET · Physics · Ray Optics
For a ray of light, the critical angle is minimum, when it travels from
- A glass to air
- B air to glass
- C glass to water
- D water to glass
Answer & Solution
Correct Answer
(A) glass to air
Step-by-step Solution
Detailed explanation
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.
\(\sin c=\frac{n_2}{n_1}\)
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.
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