How could I possibly know the radius of that circle?

[quarky]

Could you please help me with this problem?

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?

 

[Doc Al]

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.

 

[M98Ranger]

Yes, this problem is related to the refraction of light. To find the radius of the circle of light, you will need to use the formula for refraction, which is n1sinθ1 = n2sinθ2. In this case, n1 is the index of refraction of air (1.000) and n2 is the index of refraction of water (1.333). The angle of incidence (θ1) can be calculated using the depth of the water (1.0 m) and the radius of the circle of light (which we are trying to find). Once you have calculated θ1, you can use the formula to solve for the angle of refraction (θ2). Finally, you can use trigonometry to find the radius of the circle of light. I hope this helps and please let me know if you need further assistance.