In order to determine the angle of refraction, we first need to determine the index of refraction of the mineral oil. The index of refraction is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium, so we can calculate the index of refraction of the mineral oil using the formula:
n = c / v
where n is the index of refraction, c is the speed of light in a vacuum (2.99 x 108 m/s), and v is the speed of light in the mineral oil (2.17 x 108 m/s). Plugging in the given values, we get:
n = 2.99 x 108 m/s / 2.17 x 108 m/s = 1.38
Now that we know the index of refraction of the mineral oil, we can use Snell's Law to calculate the angle of refraction. Snell's Law states that the ratio of the sines of the angles of incidence and refraction is equal to the reciprocal of the index of refraction, so we can use the formula:
sin(θi) / sin(θr) = n
where θi is the angle of incidence (23.1°), θr is the angle of refraction, and n is the index of refraction (1.38). Solving for θr, we get:
sin(θr) = sin(θi) / n
Plugging in the given values, we get:
sin(θr) = sin(23.1°) / 1.38 = 0.4
Since the sine of the angle of refraction must be between 0 and 1, we know that the angle of refraction must be less than 90°. To find the exact value of the angle of refraction, we can use the inverse sine function (arcsin) to find the angle whose sine is equal to 0.4. This gives us:
θr = arcsin(0.4) = 23.8°
Therefore, the angle of refraction is 23.8°.