Question

Some biological systems can act like an optical fiber. Below is a drawing which illustrates how this might occur. Imagine you have a long, thin cell surrounded by fluid with index of refraction 1.38. The average index of refraction inside the cell is 1.48. Compute the critical angle, theta_crit, for total internal reflection for this system. Show all of your computations. What will the angle of refraction be for ray A (shown below) that has an angle of incidence of 13 degrees? Show all of your calculations. Indicate the new ray's direction and its angle of refraction on your drawing. You can draw in the angles approximately. Will rays B, C, or D undergo total internal reflection? Their angles of incidence are shown to be 50, 60, and 70 degrees. Comment on how all this relates to the idea that the rod cells (appropriately named) in our eyes can function as fiber optics.

Answer 1

a) The critical angle is: i_c = sin^-1 (n_2/n_1) = sin^-1 (1.38/1.48) = 68.8 degree = 69 degree b) Apply Snell's law: n_fluid sin i = n_cell sin r r = sin^-1 (n_fluid sin i/n_cell) = sin^-1 (1.38 sin 13/1.48) = 12 degree c) The rays which incident with critical angle or greater than the critical angle, then the light ray suffers total internal reflection. Thus, the D ray suffers total internal reflection. d) The rod cells transmit light rays through them by total internal reflection.