Question

A ray of light is incident on a glass slab of refractive index 1.52. if the reflected and refracted rays of light are mutually perpendicular to each other then the angle of incidence will be

• A. ${90}^{\circ }$
• B. ${60}^{\circ }$
• C. ${56}^{\circ }{40}^{{}^{\prime }}$
• D. ${19}^{\circ }{58}^{{}^{\prime }}$

Answer 1

Answer: (C)

${56}^{\circ }{40}^{{}^{\prime }}$

Given,
$refractiveindexn=\frac{\sin \left(i\right)}{\sin \left(r_2\right)}=1.52;.....\left(1\right)$
$i=r_1;now,reflected\&refractedrayaremutuallyperpendicular$
$\Rightarrow (90-r_1)+(90-r_2)=90\Rightarrow r_1{+r}_2=90\Rightarrow i+r_2=90$
$\Rightarrow r_2=90-i;substitutinginequation\left(1\right);$
$\Rightarrow \frac{sin\left(i\right)}{sin(90-i)}=\frac{sin\left(i\right)}{cos\left(i\right)}=tan\left(i\right)=1.52;$

$\Rightarrow i={tan}^{-1}\left(1.52\right)={56}^o{40}^{\prime }$