The Wavelength of Light in a Medium with μ = 3/2

To determine the wavelength of light in a medium with a given refractive index, we can use the formula:

λ = λ₀ / μ

where λ is the wavelength in the medium, λ₀ is the wavelength in vacuum or air, and μ is the refractive index of the medium.

Given that the wavelength of light in air is 300 nm, we need to find the wavelength in a medium with a refractive index of μ = 3/2.

Step 1: Convert the given wavelength in air to meters.

λ₀ = 300 nm = 300 × 10^(-9) m

Step 2: Substitute the values into the formula.

λ = (300 × 10^(-9) m) / (3/2)

Step 3: Simplify the expression.

λ = (300 × 10^(-9) m) × (2/3)

λ = 200 × 10^(-9) m

Step 4: Convert the wavelength back to nanometers.

λ = 200 × 10^(-9) m = 200 nm

Explanation:

When light passes from one medium to another, its wavelength changes due to the change in the speed of light in different media. The refractive index of a medium is a measure of how much the speed of light is reduced when it passes through that medium.

In this case, the refractive index of the medium is given as μ = 3/2. The formula λ = λ₀ / μ allows us to calculate the wavelength of light in the medium using the known wavelength in air (λ₀).

By substituting the given values into the formula and simplifying the expression, we find that the wavelength of light in the medium with a refractive index of μ = 3/2 is 200 nm.

This means that the light waves in the medium with a refractive index of 3/2 have a shorter wavelength compared to the wavelength in air. The change in wavelength is due to the change in the speed of light as it passes through the medium.

It is important to note that the refractive index of a medium depends on its physical properties, such as the density and composition. Different materials have different refractive indices, which determine how light interacts with and travels through them.