Question

A ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and refracted ray are mutually perpendicular, then the angle of incidence is

• A. ${58}^o{15}^{\prime }$
• B. ${57}^o{19}^{\prime }$
• C. ${58}^o{19}^{\prime }$
• D. ${57}^o{12}^{\prime }$

Answer 1

The correct option is C ${58}^o{19}^{\prime }$

Given
$i+r+{90}^{\circ }={180}^{\circ }$

$i+r={90}^{\circ }$

Where,
$i=$ angle of incidence $=$ angle of reflection

$i=$ angle of refraction.

$\mu =\frac{sini}{sinr}=\frac{sini}{sin({90}^{\circ }-i)}$

$=\frac{sini}{cosi}=tani$

or $i=ta{n}^{-1}\mu$

$=ta{n}^{-1}\left(1.62\right)$

$={58}^{\circ }{19}^{\prime }$