A headlight runs on three 1.5V AAA alkaline batteries. It is specified to give 0.25 lux at 2 m and can last for 75 hours. You are wearing the headlight and reading a map a. Calculate the illuminance (in lux) on a map located 50 cm away from your head, where the angle between the normal of the map and the direction of light is 20°.
b. Calculate the luminous flux (in lumen) of the headlight if the light is projected uniformly in a cone with an angle between the sides of 160°. See the diagram below.
c. Calculate the luminous efficacy of the lamp (in lm/W) if a typical AAA alkaline battery has a capacity of 1 Ah (Ampere hour).