Question

Light of frequency $$\nu$$, wave length $$\lambda$$ travelling with a velocity $$v$$ enters into a glass slab of refractive index $$\mu$$ then frequency, wave length and velocity of the wave in glass slab respectively are :

A
νμ, λ, vμ
B
ν, λμ, vμ
C
ν, λ, vμ
D
νμ, λμ, ν

Solution

The correct option is B $$\nu$$, $$\dfrac{\lambda }{\mu }$$, $$\dfrac{v}{\mu }$$We will use 3 concepts in this question:1. Frequency of light does not change when light passes from one medium to another. Hence, when light enters a glass slab, it's frequency remains the same. $$\nu_1 = \nu_2$$2. Refractive Index of medium 2 wrt medium 1 = (velocity of light in medium 1) / (velocity of light in medium 2) $$\mu = \dfrac{v_1}{v_2}$$As we know $$\nu= v \lambda \implies v_{1} {\lambda}_1=v_2 {\lambda}_2$$ as $$\nu_1 =\nu_2$$Hence,$$\dfrac{v_1}{\lambda_1} = \dfrac{v_2}{\lambda_2}$$Rearrange$$\dfrac{\lambda_1}{\lambda_2} = \dfrac{v_1}{v_2} = \mu$$Hence, $${\lambda}_2 = \dfrac{\lambda_1}{\mu}$$Now for velocity:Use $$\lambda_2$$ in formula 2$$v_2 = \dfrac{\mu}{\lambda_2}$$Physics

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