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Q.

A beam of light passes from air into a substance M, If the angle of incidence is $40 °$ and the angle of refraction is $30 °$ , calculate the refractive index of the substance (given $\sin 40 ° = 0.6428$ , $\sin 30 ° = 0.5000$ )

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a

2.28

b

1.28

c

1.54

d

1.76

answer is B.

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Detailed Solution

The refractive index of the substance is

1.28

.
To find the refractive index of the medium in this case, we will use Snell's Law.
Snell's Law states that "the ratio of the sine of the angle of incidence to the sine of the angle of refraction is always constant and equal to the relative refractive index of the media."

\frac{sin i}{sin r} = n_{21}

\Rightarrow \frac{sin i}{sin r} = \frac{n_{2}}{n_{1}}

Substituting the values of angle of incidence, angle of refraction and refractive index of air (1).

\Rightarrow \frac{\sin 40 º}{\sin 30 º} = \frac{n_{2}}{1}

\Rightarrow \frac{0.6428}{0.5000} = \frac{n_{2}}{1}

\Rightarrow n_{2} = 1.28

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