A Streetlight contains two identical bulbs

Question

A streetlight contains two identical bulbs 3.3 m above the ground. If the community wants to save electrical energy by removing one bulb, how far from the ground should the streetlight be positioned to have the same illumination on the ground under the lamp?

____________m

Answer 1

Let E = light energy incident on the road from each bulb

=> total intensity = 2E / 4π(3.3)^2

If d = distance at which a single bulb should be positioned, then

intensity will be E/4πd^2

For both intensities to be equal,

2E / 4π(3.3)^2 = E/4πd^2

=> d^2 = (3.3)^2 / 2

=> d = 3.3 / √2 = 2.12 m.