\(\text{ Light is incident on an interface between water } (\mu = \frac{4}{3}) \text{ and glass } (\mu = \frac{3}{2}).\\\) \(\text{For total internal reflection, light should be traveling from:}\)
- \(\quad \text{water to glass and } \angle i > \angle i_c \\\)
- \(\quad \text{water to glass and } \angle i < \angle i_c \\\)
- \(\quad \text{glass to water and } \angle i < \angle i_c \\\)
- \(\quad \text{glass to water and } \angle i > \angle i_c\)
The Correct Option is D
Approach Solution - 1
To determine the correct condition for total internal reflection at an interface between two media, we need to consider the refractive indices and the direction of light travel. The phenomenon of total internal reflection occurs when light travels from a medium with a higher refractive index to a medium with a lower refractive index, and the incidence angle exceeds the critical angle.
For the given problem:
1. Refractive index of water, \(\mu_{\text{water}}=\frac{4}{3}\).
2. Refractive index of glass, \(\mu_{\text{glass}}=\frac{3}{2}\).
Since glass has a higher refractive index than water (\(\mu_{\text{glass}} > \mu_{\text{water}}\)), total internal reflection can only occur when light travels from glass to water.
The condition for total internal reflection is that the angle of incidence \(\angle i\) must be greater than the critical angle \(\angle i_c\). The critical angle can be calculated from:
\[\sin(\angle i_c)=\frac{\mu_{\text{water}}}{\mu_{\text{glass}}}=\frac{4}{3}/\frac{3}{2}=\frac{8}{9}\]
Therefore, \(\angle i_c\) is the angle whose sine is \(\frac{8}{9}\), and total internal reflection occurs when:
\(\quad \text{light travels from glass to water and } \angle i > \angle i_c\)
Approach Solution -2
\(\text{Total internal reflection occurs when light travels.}\)
\(\text{From a denser medium to a rarer medium and the angle of incidence exceeds the critical angle.}\)
\(\\ \text{Here, glass } (\mu = \frac{3}{2}) \text{ is denser than water } (\mu = \frac{4}{3}). \text{ So, for total internal reflection, the light should be traveling from glass to water}\\ \text{and the angle of incidence should be greater than the critical angle } \angle i_c.\)
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