# How could I possibly know the radius of that circle?

1. Jul 21, 2004

### quarky

Light coming from an underwater source emerges from the surface in a circle. If the water is 1.0 m deep and its index of refraction is 1.333, how big is this circle of light?

Is this related to refraction of light? If so, how could I possibly know the radius of that circle?

2. Jul 21, 2004

### Staff: Mentor

total internal reflection

Imagine a point source of light 1.0 m below the water surface. It's emitting light in all directions. When that light hits the water-air surface, depending on the angle of incidence, it will be refracted into the air. But will all the light that hits the surface refract? No. Some light will be reflected back into the water.

Consider Snell's law of refraction $n_1sin\theta_1 = n_2sin\theta_2$. When going from a medium of higher refractive index to one of lower refractive index (like going from water [n=1.33] to air [n=1]) there is a maximum angle of incidence that will allow refraction. Light hitting at a greater angle will not refract, but instead will reflect back into the water. Find that maximum angle (called the critical angle) and use it to find the size of the circle.