HSC Science (Computer Science) 12th Board ExamMaharashtra State Board
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Solution - Determine the change in wavelength of light during its passage from air to glass. If the refractive index of glass with respect to air is 1.5 and the frequency of light is 3.5 x 1014 Hz - HSC Science (Computer Science) 12th Board Exam - Physics

Question

Determine the change in wavelength of light during its passage from air to glass. If the refractive index of glass with respect to air is 1.5 and the frequency of light is 3.5 x 1014 Hz, find the wave number of light in glass.

[Velocity of light in air c = 3 x 108 m/s]

Solution

Given: μg = 1.5, n=4 × 1014Hz, c = 3 × 108m/s

The wavelength of light incident on glass from air is

`lambda=c/n=(3 xx 10^8)/(3.5 xx 10^14)=8.571 xx 10^-7 m=8571 xx 10^-10 m=8571Å`

Now, the velocity of light in glass is given from its refractive index as

`mu_g = c/(v_g)`

We also know that velocity is product of frequency and wavelength.

∴`mu=c/(v_g)=(nlambda_a)/(nlambda_g)=lambda_a/(lambdag)`

∴`lambda_g=lambda_a/mu_g=8571 /1.5=5714`Å

Therefore, the difference in wavelength is

`lambda_a-lambda_g=8571 - 5714 = 2857`Å

The wave number is the reciprocal of the wavelength

Therefore, the wave number in glass is

`barlambda_g=1/lambda_g`

∴`barlambda_g=1/(5.714 xx 10^-7)=1.75 xx 10^6m^-1`

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Reference Material

Solution for question: Determine the change in wavelength of light during its passage from air to glass. If the refractive index of glass with respect to air is 1.5 and the frequency of light is 3.5 x 1014 Hz concept: Reflection and Refraction of Plane Wave at a Plane Surface Using Wave Fronts. For the courses HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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