4-1. Lighting (23 points total) Given a living room with a dimension of 5 m by 6 m with a height of 2.5 m. There is a ceiling lamp in the middle of the ceiling with a conical lamp shade with an angle of 160 between the two sides. Assume you use an 901m/W LED lamp where the light intensity is uniformly distributed within the lamp shade. Ignore the effect of the walls. a. If the illuminance on the floor at the center of the room is 100 lux, calculate the luminous flux and electric power that is needed for the LED lamp. b. Derive an equation for the illuminance at any location (x, y) on the floor. Use a graphing software (e.g. excel) to draw a 3-D surface plot or a 2-D contour plot of the illuminance profile on the floor. What is the illuminance (in lux) on the floor at the corner of the room? c. Light uniformity of light is defined as the minimum E over the average E. Calculate the average illuminance on the floor and estimate the light uniformity in this room