Question

Light passes from air into a liquid and is deviated 19° when the angle of incidence is 52°.What is the index of refraction of the liquid ?Sin 52° = 0.7880 sin 33° = 0.5446.

Answer 1

As Light passes from air into a liquid the deviation = i-r
so i - r = 19°
and i = 52°
so r = 52 -19 = 33°
so refractive index of the liquid = sini/sinr = sin52°/sin33° = 0.7880/0.5446 = 1.45 (approx)

Answer 2

Given :

Angle of incidence (i) = 52°

To Find :

Index of refraction of the liquid

Solution :

As the ray of light is passing from air to liquid i.e., from rarer to denser medium, it will bent towards the normal. Thus,

Angle of refraction (r) = 52° - 19° = 33°

Let the refractive index of air and liquid be 'μ₁' and 'μ₂' respectively.

Using Snell's Law,

      Sin i × μ₁   =  Sin r × μ₂

⇒ Sin 52 × 1     =  Sin 33 °× μ₂

⇒          μ₂        =   $\frac{Sin 52}{Sin 33}$

⇒          μ₂        =  $\frac{0.7880}{0.5446}$

∴           μ₂        =  1.45

Hence, the index of refraction of the liquid is 1.45