How bright would the sun appear to be to an observer on Earth if the Sun were four times farther from the Earth than it actually is?Please express...

Let the distance between the sun and the earth be
x.

Let the light energy received by the earth rom the sun
be L.

If the distance of the sun from earth becomes four
times, then obviously the time taken by the light wave to reach earth increases four
times.

We know that
frequency(v)=1/T.

and speed of
light(c)=v*wavelength.

c is constant and is equal to
299792458 m/s.

So, frequency is inversely proportional to
the wavelength.

So, if the time increases four times,
frequency(v) decreases 4 times and the wavelength simultaneously increases four
times.

Hence, the wavelength of the light would
become four times the wavelength of the visible part of the electromagnetic spectrum i.e
4 times of 4000 to 8000 Angstorm. Now, the wavelength would be in the range of 16000 to
32000 Angstorm, which is not perceptible by the naked human
eye.

Hence, the earth would receive the waves
which are not optically perceptible by the
humans.

Hope it
helps.

Thanx.