Physics - Geometrical Optics Question with Solution | TestHub

PhysicsGeometrical OpticsTIR/Prism and DispersionEasy2 minPYQ_2020

PhysicsEasysingle choice

A transparent cube of side $d$ , made of a material of refractive index $μ_{2}$ , is immersed in a liquid of refractive index $μ_{1} (μ_{1} < μ_{2})$ . A ray is incident on the face $A B$ at an angle $θ$ (shown in the figure). Total internal reflection takes place at the point $E$ on the face $B C .$

Then, $θ$ must satisfy

Options:

Answer:

Solution:

At surface (1)

$μ_{1} \sin θ = μ_{2} \sin r \dots (1)$

At surface (2)

$μ_{1} = μ_{2} \sin (90 - r)$

$μ_{1} = μ_{2} \cos r . . . (2)$

From equation $(1)$ and $(2)$

$\Rightarrow \sin θ = \frac{\sin r}{\cos r}$

$\Rightarrow \sin θ = \frac{\frac{(\sqrt{μ_{2}^{2} - μ_{1}^{2}})}{μ_{2}}}{(\frac{μ_{1}}{μ_{2}})}$

$\Rightarrow \sin θ = \sqrt{\frac{μ_{2}^{2}}{μ_{1}^{2}} - 1}$

$θ$ must satisfy,

$\Rightarrow θ < \sin^{- 1} (\sqrt{\frac{μ_{2}^{2}}{μ_{1}^{2}} - 1})$

Subject:PhysicsTopic:Geometrical OpticsSubtopic:TIR/Prism and Dispersion

⏱ 2mℹ️ Source: PYQ_2020

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