The refractive indices of two media are denoted by n 1 and n 2 and t

The refractive indices of two media are denoted by n1 and n2 and the velocities of light in these two media are respectively v1 and v2. If n2 / n1 is 1.5, which one of the following statements is correct?

v<sub>1</sub> is 1.5 times v<sub>2</sub>.
v<sub>2</sub> is 1.5 times v<sub>1</sub>.
v<sub>1</sub> is equal to v<sub>2</sub>.
v<sub>1</sub> is 3 times v<sub>2</sub>.
This question was previously asked in
UPSC NDA-2 – 2018
The correct statement is that v₁ is 1.5 times v₂.
– The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v). That is, n = c/v.
– For two media, we have n₁ = c/v₁ and n₂ = c/v₂.
– The given relation is n₂ / n₁ = 1.5.
– Substitute the expressions for n₁ and n₂: (c/v₂) / (c/v₁) = 1.5.
– This simplifies to (c/v₂) * (v₁/c) = v₁ / v₂ = 1.5.
– Rearranging the equation, we get v₁ = 1.5 * v₂.
– A higher refractive index means light travels slower in that medium.
– Since n₂/n₁ = 1.5 > 1, it means n₂ > n₁. Therefore, light travels slower in medium 2 (v₂) than in medium 1 (v₁).
– The relationship v₁ = 1.5 v₂ confirms that v₁ is greater than v₂.
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