Chapter 22, Problem 45P

& Rain sensor Many cars today are equipped with a rain sensor that automatically switches on the windshield wipers when rain starts to fall. The most common modern rain sensors are based on the principle of total internal reflection. Light from an LED is beamed at a $45**\#x00B0;$ angle onto the windshield glass using a semicircular piece of glass that is glued on the windshield from inside the car When there is no ram, the light beam undergoes total internal reflection and illuminates the detector (see Figure P22.45a). If the glass is wet. the condition for total internal reflection is no longer fulfilled, and some light escapes to the outside (see Figure P22.45b). This results in a decrease in the light intensity at the detector, which is used as a signal to the car electronics to switch on the wipers Determine the range of values of the index of refraction of the windshield glass (i.e., the minimum and the maximum values) that will allow the described operation of the sensor shown in the figure.