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# Light of wavelength 2400 x 10-10 m in air will become light of wavelength in glass (µ = 1.5) equal to

Light of wavelength 2400 x 10-10 m in air will become light of wavelength in glass (μ = 1.5)
equal to
A. 1600 x 10-10 m B. 7200 x 10-10 m C. 1080 x 10-10 m D. none of these

The speed of light in vacuum is equal to the product of the  index of refraction and the speed of light through that substance.   c = n1v1 = n2v2  , since the frequency is constant then the product of wavelength through a medium and its index of refraction in that medium is equal to its wavelength in new medium and its new index of refraction,  n1x1 = n2x2.  The answer is A, 2400/1.5  = 1600.

When light enters  a denser medium its speed (v) decreases μ times (see Huygens's principle).Thus, its wavelength equals

λ = vT, where T is the period inversely proportional to the frequency.

But  v = c/μ, where c  is the speed of light in vacuum. Thus, to calculate new wavelength simply divide 2400 x10-10 by 1.5 and you will get 1600 x10 -10 m.

v = λf

Since the frequency f won't change from air to the glass, λ is proportional to v, which is inversely proportional to μ.

Therefore, the wavelength in glass = 2400 x 10^-10 (1/1.5) = 1600 x 10^-10 m.