A beam of light passes from air into a substance X. If the angle of incidence is 45 and the angle of refraction is 30, then the refractive index will be :

Foundation

Physics Foundation

Refraction and parallel slab

Question

1.42.

1.33.

0.45.

2.42.

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To find the refractive index of substance X, we use Snell's Law: $n_{1} \sin θ_{1} = n_{2} \sin θ_{2}$ . Here, $n_{1} = 1$ (air), $θ_{1} = 45 °$ , and $θ_{2} = 30 °$ . The refractive index of X is $n_{2}$ .

Substituting the values: $1 \times \sin 45 ° = n_{2} \times \sin 30 °$ .

We know $\sin 45 ° = \frac{\sqrt{2}}{2}$ and $\sin 30 ° = \frac{1}{2}$ . Therefore, $n_{2} = \frac{\frac{\sqrt{2}}{2}}{\frac{1}{2}} = \sqrt{2} \approx 1.414$ .

The final answer is 1.42.