Wave Optics

For light reflecting from air-water boundary:
- Frequency remains unchanged on reflection and refraction.
- In air, wavelength is given as $\lambda = 589\,\text{nm}$.

### (a) Reflected light
Since reflection does not change the medium,
- wavelength = $589\,\text{nm}$
- frequency = $\dfrac{c}{\lambda} = \dfrac{3.0\times10^8}{589\times10^{-9}} \approx 5.09\times10^{14}\,\text{Hz}$
- speed = $3.0\times10^8\,\text{m s}^{-1}$

### (b) Refracted light in water
Using $n = \dfrac{c}{v}$,
$$v = \frac{c}{n} = \frac{3.0\times10^8}{1.33} \approx 2.26\times10^8\,\text{m s}^{-1}$$
Frequency remains the same, so
$$\nu \approx 5.09\times10^{14}\,\text{Hz}$$
Wavelength in water is
$$\lambda' = \frac{v}{\nu} = \frac{2.26\times10^8}{5.09\times10^{14}} \approx 4.44\times10^{-7}\,\text{m} = 444\,\text{nm}$$
So the refracted light has smaller wavelength and lower speed, but the same frequency.

The shapes of the wavefronts are:

(a) Light diverging from a point source: a spherical wavefront.

(b) Light emerging out of a convex lens when a point source is placed at its focus: a plane wavefront.

(c) The portion of the wavefront of light from a distant star intercepted by the Earth: a plane wavefront.

Speed of light in a medium is
$$v = \frac{c}{n}$$
Given $c = 3.0\times10^8\,\text{m s}^{-1}$ and $n = 1.5$,
$$v = \frac{3.0\times10^8}{1.5} = 2.0\times10^8\,\text{m s}^{-1}$$
So the speed of light in glass is **$2.0\times10^8\,\text{m s}^{-1}$**.

No, the speed of light in glass is not independent of colour because glass shows dispersion. Different colours travel at different speeds in glass.

Between red and violet, violet travels slower in a glass prism, and red travels faster.