In order to initiate a process operation, an infrared motion sensor (radiation detector) is employed to determine the approach of a hot part on a conveyor system. To set the sensor's amplifier discriminator, the engineer needs a relationship between the sensor output signal, S. and the position of the part on the conveyor. The sensor output signal is proportional to the rate at which radiation is incident on the sensor.

(a) For Ld = 1 m, at what location x1 will the sensor signal S1 be 75% of the signal corresponding to the position directly beneath the sensor, So (x = 0)?

(b) For values of Ld = 0.8. 1.0, and 1.2 m, plot the signal ratio, S/So, versus part position, x, for signal ratios in the range from 1.0 to 0.2. Compare the x-locations for which S/So = 0.75.

Motion sensar. S Ly= 1m Hot part Comeyor