SATHEE: Modern Physics 7 Question 21

Modern Physics 7 Question 21

22. An electromagnetic wave of intensity $50 W m^{- 2}$ enters in a medium of refractive index ’ $n$ ’ without any loss. The ratio of the magnitudes of electric fields and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by

(a) $\frac{1}{\sqrt{n}}, \sqrt{n}$

(b) $(\sqrt{n}, \sqrt{n})$

(d) $\sqrt{n}, \frac{1}{\sqrt{n}}$

(Main 2019, 11 Jan I)

Show Answer

Solution:

In the free space, the speed of electromagnetic wave is given as,

$c = \frac{1}{\sqrt{μ_{0} ε_{0}}} = \frac{E_{0}}{B_{0}}$

where, $E_{0}$ and $B_{0}$ are the amplitudes of varying electric and magnetic fields, respectively.

Now, when it enters in a medium of refractive index ’ $n$ ‘, its speed is given as,

$v = \frac{1}{\sqrt{μ ε}} = \frac{1}{\sqrt{K ε_{0} μ}} = \frac{E}{B}$

where, $K$ is dielectric strength of the medium.

Using Eqs. (i) and (ii), we get

$\frac{v}{c} = \frac{1}{\sqrt{K}}$

$(∵$ For a transparent medium, $μ_{0} \approx μ)$

Also, refractive index of medium is ’ $n$ ’ and is given as

$\frac{c}{v} = n or \frac{v}{c} = \frac{1}{n}$

$∴$ From Eqs. (iii) and (iv), we get

$n = \sqrt{K} or K = n^{2}$

The intensity of a EM wave is given as,

$I = \frac{1}{2} ε_{0} E_{0}^{2} c$

and in the medium, it is given as $I^{'} = \frac{1}{2} K ε_{0} E^{2} v$

It is given that, $I = I^{'}$

$\Rightarrow \frac{1}{2} ε_{0} E_{0}^{2} c = \frac{1}{2} K ε_{0} E^{2} v$ or $\frac{E_{0}}{E}^{2} = \frac{K v}{c}$

From Eqs. (iv), (v) and (vi), we get

$\frac{E_{0}}{E}^{2} = \frac{n^{2}}{n} = n or E_{0} / E = \sqrt{n}$

Similarly, $\frac{1}{2} \cdot \frac{B_{0}^{2}}{μ_{0}} c = \frac{1}{2} \cdot \frac{B^{2}}{μ_{0}} v \Rightarrow \frac{B_{0}}{B} = \frac{1}{\sqrt{n}}$

Alternate method

We know that,

$\frac{E_{0}}{B_{0}} = c air/vacuum \frac{E}{B} \underset{medium}{} = v$

$\begin{aligned} Also, & n & = \frac{c}{v} \\ \frac{E_{0} / B_{0}}{E / B} & = \frac{c}{v} = n \\ \Rightarrow & \frac{E_{0} / E}{B_{0} / B} & = n \end{aligned}$

This is possible only if $\frac{E_{0}}{E} = \sqrt{n}$ and $\frac{B_{0}}{B} = \frac{1}{\sqrt{n}}$ .

पिछला

अगला

Modern Physics 7 Question 21

Solution:

Alternate method

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Modern Physics 7 Question 21

22. An electromagnetic wave of intensity 50Wm−2 enters in a medium of refractive index ’ n ’ without any loss. The ratio of the magnitudes of electric fields and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by

Solution:

Alternate method

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu