If the critical angle for total internal reflection from a...

If the critical angle for total internal reflection from a medium to vacuum is $30^{\circ}$ then velocity of light in the medium is $-\mathrm{ms}^{-1}\left(\right.$ take $\left.\mathrm{c}=3.0 \times 10^{8} \mathrm{~ms}^{-1}\right)$ (A) $2.0 \times 10^{8}$ (B) $1.5 \times 10^{8}$ (C) $10^{8}$ (D) $1.5 \times 10^{-8}$

If the critical angle for total internal reflection from a medium to vacuum is $30^{\circ}$ then velocity of light in the medium is $-\mathrm{ms}^{-1}\left(\right.$ take $\left.\mathrm{c}=3.0 \times 10^{8} \mathrm{~ms}^{-1}\right)$
(A) $2.0 \times 10^{8}$
(B) $1.5 \times 10^{8}$
(C) $10^{8}$
(D) $1.5 \times 10^{-8}$

Key Concepts

Total Internal Reflection

Total internal reflection occurs when light attempts to move from a medium with a higher refractive index to one with a lower refractive index at an incidence angle greater than a specific threshold. Under these conditions, instead of refracting out of the denser medium, the light is entirely reflected back into it.

Critical Angle

The critical angle is the minimum angle of incidence for which total internal reflection occurs when light passes from a denser medium into a less dense medium. It is determined by the refractive indices of the two media, and is given by the relationship sin?c = n?/n?, where n? is the refractive index of the less dense medium and n? is that of the denser medium.

Refractive Index

The refractive index is a measure of how much a medium slows down light compared to its speed in vacuum. It plays a crucial role in determining the bending of light at the interface between two media and is directly related to the speed of light in the medium by the formula v = c/n.

Snell's Law

Snell's Law describes the relationship between the incidence and refraction angles and the refractive indices of two media. Expressed mathematically as n? sin?? = n? sin??, it underpins the derivation of the critical angle for total internal reflection.

Speed of Light in a Medium

The speed of light in any medium is less than its speed in vacuum, and this reduction is quantified by the medium’s refractive index. The relationship is given by v = c/n, where c is the speed of light in vacuum and n is the refractive index of the medium.

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