Question

On a clear moonless night with no artificial illumination, the intensity of starlight and airglow is 2×10^−8 times that due to full sunlight. Suppose that you go outside on such a night and set a white golf ball on a dark surface, and then stand 10 m away from it. Your eye is capable of detecting light intensities as low as 2 × 10^−16 W. Will you be able to discern the white ball without the use of any artificial light, using your naked eye?

Answer 1

Moonless night with airglow uses rod-mediated vision. This table will help with a general understanding of what we are talking about here.

Now going to the problem,

We are given,

Let x be the intensity due to sunlight,

Now, the intensity of starlight and airglow =

by looking through the externally available data, I am able to get the value of x as 1050

At 10m distance assuming the light is reflected from the golf ball isotropically, the area illuminated =

=12.56

The corresponding radiant flux =

=0.02637 W

This well above the detection limit of the eye, So we will be able to see the white ball.