JEE Main · 2019 · 11 Jan 2019 · Shift 1 · EM Waves

An electromagnetic wave of intensity

50 Wm^{- 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) $(\frac{1}{n}, \frac{1}{n})$
(B) $(n, n)$
(C) $(n, \frac{1}{n})$ ✓ Correct
(D) $(\frac{1}{n}, n)$

Answer: (C)

Solution

With no loss the intensity is unchanged. Writing

I = \frac{1}{2} ε_{0} c E_{0}^{2}

in vacuum and

I = \frac{1}{2} ε_{0} n c E_{m}^{2}

in the medium (using

v = c / n

and

ε = ε_{0} n^{2}

), equality gives

E_{m} = \frac{E _{0}}{n}

, so the ratio of electric fields before to after is

n

. Since

B = E / v

B_{m} = n B_{0}

, and the ratio of magnetic fields before to after is

\frac{1}{n}

, giving the pair

(n, \frac{1}{n})

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Single correct option

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JEE Main · 2019 · 11 Jan 2019 · Shift 1 · EM Waves

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