A ray of light traveling in a transparent medium of refractive index $\mu$ falls on a surface separating the m

Question

A ray of light traveling in a transparent medium of refractive index $\mu$ falls on a surface separating the medium from the air at an angle of incidence of $45^{\circ}$. For which of the following values of $\mu$ can the ray undergo total internal reflection?

Accepted Answer

1. **Condition for Total Internal Reflection (TIR):** For TIR to occur, the angle of incidence ($i$) must be strictly greater than the critical angle ($i_c$). That is, $i > i_c$, which implies $\sin i > \sin i_c$.
2. **Critical Angle Formula:** The sine of the critical angle is given by the ratio of the refractive index of the rarer medium to the denser medium: $\sin i_c = \frac{\mu_{air}}{\mu_{medium}} = \frac{1}{\mu}$.
3. **Calculation:** Given that the angle of incidence $i = 45^{\circ}$, we have:
   $\sin(45^{\circ}) > \frac{1}{\mu}$
   $\frac{1}{\sqrt{2}} > \frac{1}{\mu}$
   $\mu > \sqrt{2}$
   $\mu > 1.414$
4. **Conclusion:** Among the given options, only $\mu = 1.50$ satisfies the condition $\mu > 1.414$.

Step-by-Step Solution

Practice All PHYSICS Questions