MCQ
A glass prism whose cross-section is an isosceles  triangle stands with its (horizontal) base in water; the angles that its two equal sides make with the base are each $\theta$. An incident ray of light, above and parallel to the water surface is totally internally reflected at the glass-water interface and subsequently re-emerges into the air. Take the refractive indices of glass and water to be $\frac{3}{2}$ and $\frac{4}{3} $ , respectively. Maximum value of $cos\theta$ is.        
  • A
    $\sqrt {\frac{{20}}{{21}}}$
  • $\sqrt {\frac{{17}}{{21}}}$
  • C
    $\sqrt {\frac{{7}}{{10}}}$
  • D
    $\sqrt {\frac{{4}}{{9}}}$

Answer

Correct option: B.
$\sqrt {\frac{{17}}{{21}}}$
b
$\alpha  + \theta  > {i_C}$

Where ${i_C}$ is critical angle for glass-water interface 

$\theta  > {i_C} - \alpha $              .........$(i)$

For air glass interface

$\sin \left( {{{90}^o} - \theta } \right) = {\mu _g}\sin \alpha $               .............$(ii)$

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