Question

Calculate the refractive index of a liquid with respect to air applying Snell's law (Use Geometric construction)

Answer is 1.19

Show all the steps​

Answer 1

Explanation:

This was a question in our school prelim paper too. ICSE 10th.

In air you will see that they have not provided the angle of incidence you have to find it

Angle of Incidence = 90 - 30 degree = 60 degrees

why?

because the normal  is perpendicular to plane.

Now they have given the angle of refraction = 45 degrees

Snell's law states that the ratio of the sines of the angles of incidence and refraction of a wave are constant when it passes between two given media.

therefore,

μ = $\frac{sin60}{sin45}$

sin60 = $\frac{\sqrt{3}}{2} }$

sin45 = $\frac{1}{\sqrt[]{2}}$

On solving you will get,

$\sqrt\frac{3}{2}$ = 1.19 approx.

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Answer 2

$ref \: index = \frac{ \sin(60) }{ \sin(45) } \\ \\ = \frac{ \sqrt{3} }{2 } \times \frac{ \sqrt{2} }{1} \\ \\ = 1.19 \: \: aprx$