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Q.

An electromagnetic wave of frequency 3×106Hz(3.0MHz) passes from vacuum into a non magnetic medium with permittivity,  ∈=16∈0, where ∈0 is the free space permittivity. The change in wavelength is

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a

-50m

b

+50m

c

-75m

d

+75m

answer is C.

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Detailed Solution

when an electro magnetic wave travels from one medium to another medium its frequency remains constant but its velocity and wavelength will change.Speed of electronmagnetic wave in vacuum is  C=1μ0∈0=fλWhere 'f' is frequency and 'λ' is wavelength of electromagnetic wave.Speed of electromagnetic wave in a medium is C'=1kμ0∈0 where ‘K’ is dielectric constantC'=fλ' where λ' is wave length of electromagnetic wave in mediumDividing the two speeds we get fλ'fλ=1k ⇒λ'=λk ⇒λ'=λ∈∈0              ∴ k=∈∈0     ⇒λ'=λ16=λ4  Change in wavelength is  λ'−λ⇒λ'−λ=λ4-λ=−34λ=−34cf               ∴λ=cf   ⇒λ'−λ=−34×3×1083×106=-34×102 ⇒λ'−λ=−75 m
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