The energy of the light reaching Earth from a "first...

The energy of the light reaching Earth from a "first magnitude" star is approximately $10^{-6}$ watts (joules per second) over each square meter of a telescope's collecting area. Assuming that this light is composed of photons of wavelength $500 \mathrm{nm},$ about how many photons are arriving in a square meter each second? How many photons enter your eye each second if your pupil is $8 m m$ in diameter?

Key Concepts

Astronomical Magnitude System

The astronomical magnitude system is a logarithmic scale used to classify the brightness of stars as seen from Earth. A 'first magnitude' star is among the brightest visible, and its light flux can be related to known energy values. Understanding the magnitude system helps in connecting observational data with measured physical quantities like energy flux.

Aperture Area Calculation

This concept is used to determine the collecting area of instruments like telescopes or the human eye. For a circular aperture, the area is calculated using A = ? (d/2)², where d is the diameter. The effective area dictates the total amount of energy (or number of photons) collected, scaling the incoming flux based on the detector’s size.

Photon Energy

This concept involves determining the energy carried by a single photon using the equation E = hc/?, where h is Planck’s constant, c is the speed of light, and ? is the wavelength. It connects the properties of light as both a wave and a particle, allowing us to convert between the energy in joules and the number of photons at a given wavelength.

Light Flux

Light flux refers to the power per unit area (measured in watts per square meter) arriving from a source. In this context, the flux value tells us how much energy passes through a unit area each second, which is key to determining how many photons are being delivered since the energy of each photon is known.

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