JEE MAIN - Physics (2023 - 31st January Morning Shift - No. 25)
In a medium the speed of light wave decreases to $$0.2$$ times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is $$x: 1$$. The value of $$x$$ is _________.
(Given speed of light in free space $$=3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}$$ and for the given medium $$\mu_{\mathrm{r}}=1$$)
Answer
5
Explanation
We know that $v=\frac{c}{n}=\frac{c}{\sqrt{\varepsilon_{r}}}$
Putting the values:
$0.2 c=\frac{c}{\sqrt{\varepsilon_{r}}}$
$\Rightarrow \sqrt{\varepsilon_{r}}=5$
$\Rightarrow$ Required ratio $=\frac{\varepsilon_{r}}{n}=\frac{\varepsilon_{r}}{\sqrt{\varepsilon_{r}}}=\sqrt{\varepsilon_{r}}=5$
$\Rightarrow x=5$
Putting the values:
$0.2 c=\frac{c}{\sqrt{\varepsilon_{r}}}$
$\Rightarrow \sqrt{\varepsilon_{r}}=5$
$\Rightarrow$ Required ratio $=\frac{\varepsilon_{r}}{n}=\frac{\varepsilon_{r}}{\sqrt{\varepsilon_{r}}}=\sqrt{\varepsilon_{r}}=5$
$\Rightarrow x=5$
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