Suppose the sun appeared to you 900 times dimmer than it does now. how far away from the sun would you be? (a) 1/9 au (b) 3 au (c) 30 au (d) 90 aus (e) 900 aus

The correct answer is option 'c': 30 AUs

Explanation:

For a spherical wave front emitted by sun with total energy 'E' the energy density over the surface when it is at a distance 'r' from the sun is given by

This energy per unit area is sensed by observer as intensity of the sun.

Let the initial intensity of sun at a distance be

Thus if the sun becomes 900 times dimmer we have

Thus the distance increases 30 times.