Critical Angle and Total Internal Reflection Explained
a) What is the minimum angle of incidence for which total internal reflection will occur at the sea surface?
a) 48.6 degrees
b) Is the given oil refractive index (1.24) the maximum or minimum value for which total internal reflection will occur at that angle of incidence? Explain.
b) The given oil refractive index of 1.24 is the minimum value for which total internal reflection will occur at that angle of incidence.
Answer:
(a) The minimum angle of incidence for total internal reflection at the sea surface is approximately 48.6 degrees.
(b) The given oil refractive index of 1.24 is the minimum value for which total internal reflection will occur at that angle of incidence.
(a) To calculate the minimum angle of incidence for total internal reflection at the sea surface, we can use Snell's law and the concept of critical angle. The critical angle is the angle of incidence at which the refracted angle becomes 90 degrees, resulting in total internal reflection.
The critical angle (θc) can be determined using the formula: θc = sin^(-1)(n2/n1), where n1 is the refractive index of the first medium (sea, n1 = 1.34) and n2 is the refractive index of the second medium (oil, n2 = 1.24).
Plugging in the values, we have: θc = sin^(-1)(1.24/1.34) ≈ 48.6 degrees. Therefore, the minimum angle of incidence for total internal reflection at the sea surface is approximately 48.6 degrees.
(b) The given oil refractive index of 1.24 is the minimum value for which total internal reflection will occur at that angle of incidence. Total internal reflection occurs when light passes from a medium with a higher refractive index to a medium with a lower refractive index, and the angle of incidence exceeds the critical angle.
If the refractive index of the oil were higher than 1.24, the critical angle would be smaller, and there would be a wider range of angles for total internal reflection to occur. However, since the oil refractive index is already at its minimum value, any further decrease in refractive index would decrease the critical angle, making it impossible for total internal reflection to occur.
In summary, the given oil refractive index of 1.24 is the minimum value for which total internal reflection will occur at the minimum angle of incidence because any lower refractive index would result in a smaller critical angle, preventing total internal reflection.