Q124 / 160 · AP EAMCET 2020 (17 Sep Shift 2) · Physics

A ray of light travels from a medium of refractive index 2 to another medium of refractive index \(\sqrt{2}\). Total internal reflection takes place when the angle of incidence is

  • A
    \(30^{\circ}\)
  • Correct answer
    B
    \(45^{\circ}\)
  • C
    \(60^{\circ}\)
  • D
    \(80^{\circ}\)

Solution

Refractive index of first medium, \(\mu_1=2\) Refractive index of second medium, \(\mu_2=\sqrt{2}\) If \(i_C\) be the angle of incidence in the case of total internal reflection, then \(\begin{array}{ll} & \quad{ }^2 \mu_1=\frac{1}{\sin i_C} \Rightarrow \frac{\mu_1}{\mu_2}=\frac{1}{\sin i_C} \\ \Rightarrow & \frac{2}{\sqrt{2}}=\frac{1}{\sin i_C} \Rightarrow \sqrt{2}=\frac{1}{\sin i_C} \\ \Rightarrow & \sin i_C=\frac{1}{\sqrt{2}} \Rightarrow \sin i_C=\sin 45^{\circ} \\ \Rightarrow \quad & i_C=45^{\circ} \end{array}\)

Hence, the correct answer is option: 'B'.

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