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QJEEM23Pha44c: JEE Main 2023 Physics - Class 12 JEEM23Pha44c Solution: In a medium the speed of light wave decreases to times to its…

In a medium the speed of light wave decreases to 0.20.2 times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is x:1x: 1 . The value of xx is _________.

(Given speed of light in free space =3×108 m s−1=3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1} and for the given medium μr=1\mu_{\mathrm{r}}=1 )

Step-by-Step Verified Solution

We know that v=cn=cεrv=\frac{c}{n}=\frac{c}{\sqrt{\varepsilon_{r}}}

Putting the values:

0.2c=cεr0.2 c=\frac{c}{\sqrt{\varepsilon_{r}}}

⇒εr=5\Rightarrow \sqrt{\varepsilon_{r}}=5

⇒\Rightarrow Required ratio =εrn=εrεr=εr=5=\frac{\varepsilon_{r}}{n}=\frac{\varepsilon_{r}}{\sqrt{\varepsilon_{r}}}=\sqrt{\varepsilon_{r}}=5

⇒x=5\Rightarrow x=5

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