Question

A star is located 100,000 light years from earth (1 light year = 10^6 m) has a power output 8 million tomes that of the Sun and with a mass 300 times that of the Sun. The intensity of the Sun's radiation at the location of the Earth is 1400W/m^2 where the average distance between the Sun and earth is 1.5x10^11m.

1. what is the power output of this star?

2. The energy of a photon (wavelength = 500nm) is given by E(photon)=hc/lamda. Assume h=6.626x10^-34J*s; c=3x10^8m/s, where light is interpreted as a stream of particles of light called photons. Find the # of photons crossing the pupil of your eye each second coming from this star. Assume a circular cross section of the pupil with a radius of 4mm

3. If density of cone cells in your eye receiving the light is 1.5 x 10^5 cones/mm^2. What is the rate at which photons arrive on a single cone cell and the resulting time between the arrival of photons on a single cell?

Answer 1

Solution of 1:

Here,
Distance to the star from Earth  
Flux or power output of the sun at Earth  
Distance to the sun from Earth
Mass of Sun
Mass of star

The flux or power output of the star is times of the at the distance from star to , therefore at the distance :

Solution of 2:

Here,
Wavelength of the light
Planck constant
Speed of light
Radius of the pupil
Area of the pupil

Energy of the photons , number of photons crossing the area per second is given by:

But energy per unit area is

Solution of 3:

Here,
Density of eye cones per area

The photons received per area per second is , then rate of photons per second per cone is given by: