Question

A point source of light is submerged 3.3 m below the surface of a lake and emits rays in all directions. On the surface of the lake, directly above the source, the area illuminated is a circle. What is the maximum radius that this circle could have? Take the refraction index of water to be 1.333.

Answer 1

Maximum Radius = 2.89m

Step-by-step explanation:

The maximum radius will be determined by the angle of incidence which is equal to the critical angle. Now, any angle larger than that will make the light to be totally internally reflected. Hence, we can figure out that angle from Snell’s law where the refracted angle is 90°, and then use the tangent function.

From Snell's law;

n_air*sin90° = n_water*sin(θ _c)

Where;

θ_c is the critical angle

Refractive index of water; n_water = 1.333

Refractive index of air;n_air = 1

Thus;

1*1 = 1.33sinθ_c

sinθ_c = 1/1.33

θ_c = sin^(-1)0.7519

θ_c = 48.76°

Like I said earlier, we'll use tangent to find the radius.

Thus;

tanθ_c = d/R

From the question, d = 3.3m

Thus;

3.3/tan48.76 = R

So, R = 2.89m