Question

A sun-like star is barely visible to naked-eye observers on earth when it is a distance of 7.0 light years, or 6.6×1016m, away. The sun emits a power of 3.8×1026W.

Using this information, at what distance would a candle that emits a power of 0.23 W just be visible?

Answer 1

Given,

distance of the star, D = 7 light years = 6.6 * 10¹⁶ m

Power emitted or energy produced per second is luminosity, L = 3.8 * 10²⁶ W

Power emitted by the candle, L' = 0.23 W

Let distance associated with candle be D'

Now,

Brightness of an object when seen from distance D is, B = L / 4D²

Now,

It is given that candle is just visible, thus brightness of both star and candle should be same

Thus,

B _star = B _candle

=> L / 4D² = L' / 4(D')²

=> L / D² = L' / (D')²

=> (D')² = (L'/L)*D²

=> D' = * D

put the values

=> D' = * (6.6 * 10¹⁶)

            = 0.246 * 10^-13 * 6.6 * 10¹⁶ = 1623.6 m

Thus, distance associated with the bulb is 1623.6 m