Question

A point source of light is located at the bottom of a steel tank, and an opaque circular card of radius is placed horizontally over it. A transparent fluid is gently added to the tank so that the card floats on the fluid surface with its center directly above the light source. No light is seen by an observer above the surface until the fluid is deep. What is the index of refraction of the fluid

Answer 1

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.

Answer 2

start by using the addition as a sign and use multiplying