Question

If the speed of light in a medium is 2 × 108 m/s the medium's index of refraction is

Answer 1

The medium's index of refraction is 1.5

Correct question : If the speed of light in a medium is 2 × 10⁸ m/s the medium's index of refraction is

Given :

The speed of light in a medium is 2 × 10⁸ m/s

To find :

The medium's index of refraction

Formula :

$\displaystyle \sf The \: medium's \: index \: of \: refraction = n = \dfrac{Speed \: of \: light \: in \: vacuum(c)}{Speed \: of \: light \: in \: medium (v)}$

Solution :

Step 1 of 2 :

Write down the speed of light in the medium

Here it is given that the speed of light in a medium is 2 × 10⁸ m/s

The speed of light in a medium = v = 2 × 10⁸ m/s

The speed of light in a vaccum = c = 3 × 10⁸ m/s

Step 2 of 2 :

Calculate the medium's index of refraction

The medium's index of refraction

$\displaystyle \sf{ = \dfrac{Speed \: of \: light \: in \: vacuum(c)}{Speed \: of \: light \: in \: medium (v)} }$

$\displaystyle \sf{ = \frac{3 \times {10}^{8} }{2 \times {10}^{8} } }$

$\displaystyle \sf{ = 1.5 }$

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Answer 2

REFRACTIVE INDEX OF MEDIUM IS 1.5

Given:

• Speed of light in medium = 2 × 10⁸ m/s

To find:

Refractive index of medium ?

Calculation:

The general expression for refractive index of a medium with respect to vacuum is as follows:

$\mu = \dfrac{speed \: of \: light \: in \: vacuum}{speed \: of \: light \: in \: medium}$

• Since speed of light in medium is always less as compared to that in vacuum, the value of $\mu$ will be always be greater than 1.

Putting the values:

$\implies \mu = \dfrac{3 \times {10}^{8} }{2 \times {10}^{8} }$

$\implies \mu = \dfrac{3 }{2 }$

$\implies \mu = 1.5$

So, refractive index of medium with respect to vacuum is 1.5