Question

Monochromatic light of frequency $5.0 \times 10^{14}$ Hz passes from air into a medium of refractive index 1.5. Find the wavelength of the light (i) reflected, and (ii) refracted at the interface of the two media.

Hint:

When light enters another medium, its frequency remains constant but its speed and wavelength change according to the refractive index.

Answer 1

Step 1: Write the relation between wavelength, speed and frequency.
The wavelength of light is given by the relation:
\[ \lambda = \frac{v}{f} \]
where $v$ is the speed of light in the medium and $f$ is the frequency of light.

Step 2: Wavelength of reflected light.
Reflected light remains in air, therefore the speed of light is $c = 3 \times 10^8\ \text{m/s}$.
\[ \lambda = \frac{3 \times 10^8}{5.0 \times 10^{14}} \] \[ \lambda = 6 \times 10^{-7}\ \text{m} \] \[ \lambda = 600\ \text{nm} \]

Step 3: Speed of light in the medium.
The speed of light in a medium is given by:
\[ v = \frac{c}{n} \] where $n$ is the refractive index.
\[ v = \frac{3 \times 10^8}{1.5} \] \[ v = 2 \times 10^8\ \text{m/s} \]

Step 4: Wavelength of refracted light.
\[ \lambda' = \frac{v}{f} \] \[ \lambda' = \frac{2 \times 10^8}{5.0 \times 10^{14}} \] \[ \lambda' = 4 \times 10^{-7}\ \text{m} \] \[ \lambda' = 400\ \text{nm} \]

Step 5: Final answer.
Wavelength of reflected light:
\[ 600\ \text{nm} \] Wavelength of refracted light:
\[ 400\ \text{nm} \]