If an optical medium possesses a relative permeability of 10/pi and relative permittivity of 1/0.0885, then the velocity of light is greater in vacuum than that in this medium by _______ times. (mu_0=4pi x 10^-7 H/m, epsilon_0=8.85x 10^-12 F/m, c=3x10^8 m/s)

The correct answer is Option 6. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q47 – JEE-MAIN 2025

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Home Physics EM WavesQuestion #175

If an optical medium possesses a relative permeability of

\frac{10}{π}

and relative permittivity of

\frac{1}{0.0885}

, then the velocity of light is greater in vacuum than that in this medium by _______ times. (

μ_{0} = 4 π \times 10^{- 7}

H/m,

ϵ_{0} = 8.85 \times 10^{- 12}

F/m,

c = 3 \times 10^{8}

m/s)

Enter Calculated Numerical Value:

Clue 1 of 3: Speed of Light in Medium

The speed of light in a medium is determined by its absolute permeability and permittivity.

🧠 Full Solution Path

Step 1: Relate Speed of Light to Material Properties✦ Active

The speed of light in vacuum is $c = \frac{1}{\sqrt{μ_{0} ϵ_{0}}}$ , and in a medium, it is $v = \frac{1}{\sqrt{μ ϵ}}$ , where $μ = μ_{r} μ_{0}$ and $ϵ = ϵ_{r} ϵ_{0}$ . The ratio of the velocity of light in vacuum to that in the medium is the refractive index $n$ .

n = \frac{c}{v} = \frac{1 / \sqrt{μ_{0} ϵ_{0}}}{1 / \sqrt{μ_{r} μ_{0} ϵ_{r} ϵ_{0}}} = \sqrt{\frac{μ_{r} μ_{0} ϵ_{r} ϵ_{0}}{μ_{0} ϵ_{0}}} = \sqrt{μ_{r} ϵ_{r}}

Step 2: Substitute Given Relative Values○ Expand

Given the relative permeability $μ_{r} = \frac{10}{π}$ and relative permittivity $ϵ_{r} = \frac{1}{0.0885}$ . Substitute these values into the derived formula for $n$ .

n = \sqrt{\frac{10}{π} \times \frac{1}{0.0885}}

💡 Teacher's Secret Hint

Pay attention to the numerical values; they are often chosen to simplify to an integer.

Step 3: Calculate the Final Ratio○ Expand

To simplify the expression, observe that $0.0885$ is approximately equal to $\frac{5}{18 π}$ . Using this approximation, we can simplify the product $μ_{r} ϵ_{r}$ .

n = \sqrt{\frac{10}{π} \times \frac{1}{5 / (18 π)}} = \sqrt{\frac{10}{π} \times \frac{18 π}{5}} = \sqrt{\frac{10 \times 18}{5}} = \sqrt{2 \times 18} = \sqrt{36} = 6

Therefore, the velocity of light is greater in vacuum than in this medium by 6 times.

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Physics Question 47 – JEE-MAIN 2025

Clue 1 of 3: Speed of Light in Medium

🧠 Full Solution Path