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Answer :
The radius of the circle of light on the surface, from which light emerges from the water, when a small underwater pool light is 2.45 m below the surface of a swimming pool with a refractive index of 1.333 (nwater), is approximately 1.69 m (option e).
When light travels from one medium to another with different refractive indices, it undergoes refraction, which causes the light rays to change direction. In this case, as the light exits the water and enters the air, it bends away from the normal, resulting in a spread of the light beam on the surface.
To determine the radius of the circle of light, we can use Snell's Law, which relates the angles of incidence and refraction to the refractive indices of the two media. By considering the light rays that are parallel to the surface of the water at the point where the light emerges, we can calculate the angle of incidence.
Using trigonometry, we find that the angle of incidence is approximately 48.53 degrees. Then, by considering the circular symmetry of the light on the surface, we can use simple geometry to calculate the radius of the circle of light as approximately 1.69 m.
Therefore, the radius of the circle of light on the surface, emerging from the water when the small underwater pool light is 2.45 m below the surface, is approximately 1.69 m (option e).
Learn more about Snell's Law here:
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