Question

The critical angle of a liquid relative to air is 30 degree . Find the refractive index of liquid.​

Answer 1

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Answer 2

The refractive index of the liquid is 2

Explanation:

Given Data:

Critical angle (C) = 30°

Find the refractive index (μ) of liquid

The angle is said to be a critical angle , when the ratio between angle of incidence and angle of refraction is 90°.

The critical angle is inversely proportional to the refractive index of the object,

The relation critical angle and refractive index can be written as

$\text{sin C} = \frac{1}{\mu}$

Substitute the value of C in above equation

$\text{sin} 30^\circ = \frac{1}{\mu}$

${\mu} = \frac{1}{\text{sin} 30^\circ}$

$\text {As per trigonometry tabular column, the value of sin} 30^\circ\ \text{is} = \frac{1}{2}$

${\mu} = \frac{1}{\frac{1}{2} }$

${\mu} = 2$

Therefore the refractive index of the liquid is 2 when their critical angle is 30°.

To Learn More ..

1)Critical angle for a medium with respect to air is 45 degree the refractive index of that medium with respect to air is

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