Final answer:
To calculate the angle of refraction of light in oil when it hits the boundary from water at a 54.3-degree angle, apply Snell's Law using the known index of refraction of water and the index of refraction for oil. If provided, use this value to solve for the refraction angle, otherwise, it indicates total internal reflection if the sine of the angle is greater than 1.
Step-by-step explanation:
To find the angle at which the light is refracted in the oil when hitting the boundary at a 54.3-degree angle in water, you use Snell's Law, which is given by n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the indices of refraction of water and oil respectively, and θ1 and θ2 are the angles of incidence and refraction. In this case, we know that the index of refraction of water (n1) is 1.33, and we need to find the index of refraction for oil (n2) to solve for the angle of refraction (θ2).
Assuming you've obtained the index of refraction for oil (let's say it is 1.40), you can rearrange Snell's Law to solve for θ2 as follows: sin(θ2) = (n1 * sin(θ1)) / n2. Plugging in the known values, sin(θ2) = (1.33 * sin(54.3°)) / 1.40. Calculate the sine of 54.3 degrees, multiply by 1.33, and divide by 1.40, then use the inverse sine to find θ2.
If after performing the calculation the value of sin(θ2) is greater than 1, this means that no refraction occurs, and total internal reflection takes place instead.