Question

5.does light travel from water into air for every angle of incidence? Explain why?

Answer 1

No. Light travels from water into air only when the angle of incidence is less than around `48.6^circ`

Explanation:

The refractive index of water is more than air. This means that when light travels from air to water, it bends towards the normal (except of course when it falls normally on the interface).

On the other hand, when traveling from water to air, it bends away from the normal. However, there is a limit to how much it can bend. After all, the angle of refraction cannot exceed `90^circ`. In the case of light traveling from water to air, when the angle of incidence is about `48.6^circ`,the angle of refraction reaches `90^circ`. At this angle of incidence, called the critical angle, the refracted ray just grazes the surface. Once the angle of incidence exceeds the critical angle, refraction is no longer possible and all the light is reflected back into the water. This phenomenon is called total internal reflection.

Snell's law tells us that if `mu` is the refractive index of water with respect to air (around 1.33 for visible light), then for light traveling from water to air, we have

`sin i/sin r = 1/mu implies sin r = mu sin i`

Since `sin r <= 1`, for refraction to occur we must have

`mu sin i <= 1 implies sin i <= 1/mu = sin theta_c`

Thus light will travel from water to air only if `i<= theta_c`. This `theta_c` is the critical angle that we were talking about above.

`color(red)(theta_c = sin^-1(1/mu))`

For water, `theta_c = sin^-1(1/1.33)~~ 48.6^circ`

Note that below the critical angle, there is always a part of the light that is reflected - and the rest is transmitted into air. The fraction of light energy that is reflected back grows with the angle of incidence and reaches 100 % at the critical angle and beyond.