If the speed of light in air is $3 \times 10^8$ m/s, then the speed of

If the speed of light in air is $3 \times 10^8$ m/s, then the speed of light in a medium of refractive index $\frac{3}{2}$ is

[amp_mcq option1=”$2 \times 10^8$ m/s” option2=”$\frac{9}{4} \times 10^8$ m/s” option3=”$\frac{3}{2} \times 10^8$ m/s” option4=”$3 \times 10^8$ m/s” correct=”option1″]

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UPSC CDS-1 – 2020

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The refractive index (n) of a medium is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in that medium (v). The formula is $n = c/v$. Given the speed of light in air (approximately equal to the speed in vacuum) $c = 3 \times 10^8$ m/s and the refractive index of the medium $n = 3/2$, we can find the speed of light in the medium ($v$) by rearranging the formula: $v = c/n$.
$v = (3 \times 10^8 \, \text{m/s}) / (3/2) = (3 \times 10^8 \, \text{m/s}) \times (2/3) = 2 \times 10^8$ m/s.

– Refractive index $n = c/v$.
– $c$ is the speed of light in vacuum (or air).
– $v$ is the speed of light in the medium.

The refractive index is a dimensionless quantity and is always greater than or equal to 1. A higher refractive index indicates a slower speed of light in the medium. The speed of light is maximum in vacuum.

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