Final answer:
To calculate the speed of light in a gemstone, Snell's Law is applied using given angles of incidence and refraction from water to the gemstone. An unreasonable result would suggest a refractive index that implies a speed of light slower than in water or faster than in a vacuum, indicating a potential error in the assumptions or angle measurements.
Step-by-step explanation:
Calculating the Speed of Light in a Gemstone
We can use Snell's Law to calculate the speed of light in a gemstone, given the angles of incidence and refraction when light passes from water into the gemstone. The law states that n1 sin(θ1) = n2 sin(θ2), where n1 and n2 are the refractive indices of water and the gemstone, respectively, and θ1 and θ2 are the angles of incidence and refraction.
For water, the refractive index n1 is approximately 1.33. The angle of incidence θ1 is 80.0° and the angle of refraction θ2 in the gemstone is 15.2°. Plugging these values into Snell's Law, we can solve for n2, the refractive index of the gemstone.
n2 = (1.33 * sin(80.0°)) / sin(15.2°)
After calculating n2, we can determine the speed of light in the gemstone, v2, using the equation v2 = c / n2, where c is the speed of light in a vacuum.
Assessment of the Results
(a) The calculated speed of light in the gemstone would result from the refractive index obtained previously. (b) The result may be unreasonable if the calculated speed of light is significantly slower than that in water or faster than in a vacuum, both of which are physically impossible. (c) The assumption that the measured angles of incidence and refraction are accurate may be inconsistent or unreasonable if they yield an impossible refractive index or speed of light.