Question

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(1) A beam of light passes from air to a medium
X. If the angle of incidence is 45° and angle of
refraction is 30°, calculate the refractive index of X.

Ans: 1.414​

Answer 1

Answer:

Since, Refractive index = sin i/sin r

$\frac{ \sin( {45}^{o} )}{ \sin( {30}^{o} ) } = \frac{1}{ \sqrt{2} } \div \frac{1}{2} = \frac{1}{ \sqrt{2} } \times 2 \\ = \frac{2}{ \sqrt{2} } = 1.414 \\ hence \: proved$

The refractive index of X is 1.414

Answer 2

Answer:

1.41 (approx.)

Explanation:

We have:

n1 (air) = 1.

n2 (medium X) = ?

Angle of incidence = 45°

Angle of refraction = 30°

To find : n2

By Snell's Law,

n1 • sin i = n2 • sin r

That is,

1 • sin 45° = n2 • sin 30°

1/√2 = n2 • 1/2

n2 = (1/√2)/(1/2) = (1/√2)×(2/1) = 2/√2 = √2 = 1.41 (approx)

Therefore,

Refractive index of medium X = 1.41 (approx.)