Final answer:
The radius of the circle seen by the diver through the water is calculated using the critical angle and trigonometry, resulting in option (a) 15 x 3 x √5 cm.
Step-by-step explanation:
The question relates to the phenomenon of refraction of light when a diver looks up through water. To find the radius of the circle that the diver sees, we can use Snell's Law and the concept of the critical angle. Since the question relates to the circular horizon that a diver sees, this involves the limits of the angle of incidence for which light can still exit the water.
The critical angle can be calculated using the formula θ_critical = arcsin(n2/n1), where n1 is the refractive index of the first medium (water, in this case) and n2 is the index of the air, which is approximately 1. Using the refractive index of water (n = 4/3), the formula simplifies to θ_critical = arcsin(3/4).
Using trigonometry, the radius (r) of the circular horizon is r = d / tan(θ_critical), where d is the depth of the diver's eyes below the water surface. Substituting the known values, the calculation gives us the radius of the horizon circle as:
r = 15 cm / tan(arcsin(3/4)) = 15 cm * (1/tan(arcsin(3/4)))
The exact value after solving this would yield the correct option, which is option (a) 15 x 3 x √5 cm.