Final answer:
The index of refraction of the fluid is 1.
Step-by-step explanation:
The index of refraction of the fluid can be found using Snell's law, which relates the angles of incidence and refraction to the indices of refraction of the two media involved. In this case, the light is traveling from the fluid (with unknown index of refraction, let's call it n2) to air (with an index of refraction of approximately 1). When the incident angle is such that the refracted angle is 90 degrees (i.e., the critical angle), total internal reflection occurs.
The critical angle can be calculated using the formula: sin(critical angle) = n1 / n2, where n1 is the index of refraction of the material the light is coming from (in this case, air). Rearranging the formula, we can solve for n2: n2 = n1 / sin(critical angle). Plug in the known values: n1 = 1 and critical angle = 90 degrees.
So, the index of refraction of the fluid is n2 = 1 / sin(90) = 1 / 1 = 1.