An owl has good night vision because its eyes can detect a...

An owl has good night vision because its eyes can detect a light intensity as small as $5.0 \times 10^{-13} \mathrm{~W} / \mathrm{m}^{2}$ What is the minimum number of photons per second that an owl eye can detect if its pupil has a diameter of $8.5 \mathrm{~mm}$ and the light has a wavelength of $510 \mathrm{~nm}$ ?

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Key Concepts

Intensity and Power

Intensity is defined as the power per unit area of a light beam. By multiplying the intensity by the area over which the light is collected, one can determine the total power incident on a detector. This relationship is critical for understanding how energy is distributed in an optical system.

Photon Energy

This concept involves calculating the energy of an individual photon using Planck's relation, E = hc/?, where h is Planck’s constant, c is the speed of light, and ? is the wavelength of the light. It forms the foundation of quantum mechanics, linking the particle-like properties of light to its wave properties.

Area Calculation for Circular Aperture

When light is collected by a circular opening, the effective area is computed using the formula for the area of a circle, A = ?*(d/2)^2, where d is the diameter. This calculation is essential in converting an intensity (power per unit area) into the total power received.

Photon Counting

This concept involves determining the number of photons detected per unit time by dividing the total power received by the energy of an individual photon. It connects macroscopic measurements of power with the microscopic existence of discrete photon packets, a key idea in photonics and quantum optics.

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