Answer:
Liquid's index of refraction, n₁ = 1.27
Explanation:
It is given that,
The critical angle for a liquid in air is, [tex]\theta_c=52^o[/tex]
We have to find the refractive index of the liquid. Critical angle of a liquid is defined as the angle of incidence in denser medium for which the angle of refraction is 90°.
Using Snell's law as :
[tex]n_1sin\theta_c=n_2sin\theta_2[/tex]
Here, [tex]\theta_2=90[/tex]
[tex]sin\theta_c=\dfrac{n_2}{n_1}[/tex]
Where
n₂ = Refractive index of air = 1
n₁ = refractive index of liquid
So,
[tex]n_1=\dfrac{n_2}{sin\theta_c}[/tex]
[tex]n_1=\dfrac{1}{sin(52)}[/tex]
n₁ = 1.269
or n₁ = 1.27
Hence, the refractive index of liquid is 1.27
