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A ray of light travelling in a transparent medium of refractive index $\mu$ falls on a surface separating the medium from air at an angle of incidence of $45^\circ$. For which of the following values of $\mu$ can the ray undergo total internal reflection?
A
$\mu = 1.25$
B
$\mu = 1.33$
C
$\mu = 1.40$
D
$\mu = 1.50$
Detailed Solution
Total internal reflection occurs when the angle of incidence exceeds the critical angle C, where $\sin C = \frac{1}{\mu}$.
Condition: $i > C$, i.e., $\sin i > \sin C = \frac{1}{\mu}$
$\mu > \frac{1}{\sin45^\circ} = \sqrt{2}$
$\mu > 1.414$
Among the given values only 1.50 is greater than 1.414.
Hence $\mu = 1.50$.
Condition: $i > C$, i.e., $\sin i > \sin C = \frac{1}{\mu}$
$\mu > \frac{1}{\sin45^\circ} = \sqrt{2}$
$\mu > 1.414$
Among the given values only 1.50 is greater than 1.414.
Hence $\mu = 1.50$.