RaySix

Post

Wavelength of light in different mediums.

Created by @nathanedwards

at November 3rd 2023, 5:45:20 pm.

AP_Physics_2-Questions

#speed-of-light

#wavelength

#refractive-index

Question:

A light wave travels from medium 1 to medium 2, experiencing a change in wavelength and speed. The wavelength in medium 1 is 600 nm, and the speed of light in medium 1 is $3.0 \times 10^8$ m/s. In medium 2, the speed of light is $2.2 \times 10^8$ m/s. Find the wavelength of the light wave in medium 2.

Answer:

The speed of light in a medium is given by the equation:

v = \frac{c}{n}

where v is the speed of light in the medium, c is the speed of light in vacuum, and n is the refractive index of the medium.

Let's calculate the refractive index, n1, of medium 1 using the given information. We are given the speed of light in medium 1, v1, as $3.0 \times 10^8$ m/s and the speed of light in vacuum as c = $3.0 \times 10^8$ m/s.

Using the equation above, we have:

n1 = \frac{c}{v1}

n1 = \frac{(3.0 \times 10^8 \, \text{m/s})}{(3.0 \times 10^8 \, \text{m/s})}

n1 = 1

Since the refractive index of medium 1, n1, is 1, it implies that medium 1 is vacuum.

Now, let's calculate the refractive index, n2, of medium 2. We are given the speed of light in medium 2, v2, as $2.2 \times 10^8$ m/s and the speed of light in vacuum as c = $3.0 \times 10^8$ m/s.

Using the equation above, we have:

n2 = \frac{c}{v2}

n2 = \frac{(3.0 \times 10^8 \, \text{m/s})}{(2.2 \times 10^8 \, \text{m/s})}

n2 \approx 1.36

Now, let's use the relationship between the refractive index and the wavelength to find the wavelength, λ2, of the light wave in medium 2.

The relationship is given by:

\frac{\lambda2}{\lambda1} = \frac{n1}{n2}

Substituting the known values, we have:

\frac{\lambda2}{600 \, \text{nm}} = \frac{1}{1.36}

To solve for λ2, we can cross multiply:

\lambda2 = 600 \, \text{nm} \times \frac{1}{1.36}

\lambda2 \approx 441 \, \text{nm}

Therefore, the wavelength of the light wave in medium 2 is approximately 441 nm.