Question

Define relative refractive index in terms of wavelength and hence show
that is =​

Answer 1

Answer:

Refractive index of a medium depends upon the refractive index of the surroundings (when you consider the light ray passing from the surrounding into the medium), optical density, wavelength of the light and temperature.

Yeah it does depend on the the wavelength of light, because:

As wavelength of light decreases, the velocity of light decreases. Now, we know, absolute refractive index of a medium is equal to the (speed of light in air)/(speed of light in that medium), therefore if the velocity of light changes, the refractive index of the medium (for that wavelength of light) also changes.

Example: it's due to this difference in velocities that dispersion of sunlight (to form rainbow) takes place. While rainbow is formed, the different colors (with different wavelengths) bend at different angles, but as all colors of light pass through same medium, thus, refractive index of medium does depend on the wavelengths.

Answer 2

Answer:

Relative Refractive Index in terms of wavelength can be defined as the ratio of speed to the product of frequency and wavelength.

Relative Refractive index, n = c/fλ

Explanation:

• A wave's wavelength is the characteristic that determines the separation between identical points in two succeeding waves.
• The distance between the two crests or troughs of the light wave is known as the wavelength of light.
• The formula that can be utilised to determine wavelength,
• v=λf where, the light's velocity is v, The light's wavelength is, and the frequency of light is f.
• The measurement of how much a light beam bends as it travels through different media is called the refractive index.
• It can alternatively be described as the difference between the speed of light in a substance and the speed of a light ray in a vacuum.

• The formula below can be used to determine a medium's refractive index: n = c/v, where n is the medium's refractive index, The speed of light in a vacuum is c, and the speed of light in the medium is v.
• Therefore, the relation in between becomes,
• Refractive index, n = c/fλ  

• The Refractive index is inversely proportional to wavelength.
• If two light waves have μ₁ and μ₂ respectively having λ₁ and λ₂ as wavelength then the relationship can become ₁μ₂ = λ₁/λ₂

Thus, the relative refractive index in terms of wavelength can be defined as n = c/fλ.

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