Question

At what distance will a 45 W lightbulb have the same apparent brightness as a 130 W bulb viewed from a distance of 35 m ? (Assume that both bulbs convert electrical power to light with the same efficiency, and radiate light uniformly in all directions.)

Answer 1

Answer:

20.6 m

Explanation:

P₁ = Power of first bulb = 45 W

P₂ = Power of second bulb = 130 W

r₁ = distance from the first bulb

r₂ = distance from the second bulb = 35 m

Using the equation

$\frac{P_{1}}{r_{1}^{2}} = \frac{P_{2}}{r_{2}^{2}}$

Inserting the values

$\frac{45}{r_{1}^{2}} = \frac{130}{35^{2}}$

r₁ = 20.6 m