Question

The minimum sensitivity of the human eye is about 1.5×10⁻¹¹ J/m²⋅s. In other words, the power input from a light source must be at least this much for the eye-brain combination to "see" the light. If the diameter of the pupil of the eye is 0.6 cm, what is the power level (in watts) actually entering the eye at the given power level? How many photons per second of wavelength 500 nm enter the eye at this intensity level?

Answer 1

To find the power level entering the eye at the given power level, use the formula Power = Energy / Time. To calculate the number of photons per second entering the eye at this intensity level, use the formula Number of photons = Power / Energy per photon.

Step-by-step explanation:

To find the power level actually entering the eye, we need to calculate the power of the light source based on the given minimum sensitivity of the human eye. The formula to calculate power is:

Power = Energy / Time

Given that the minimum sensitivity of the human eye is 1.5x10^-11 J/m²·s, we can calculate the power by substituting the given energy into the formula:

Power = 1.5x10^-11 J/m²·s / 1 second

Therefore, the power level entering the eye at the given power level is 1.5x10^-11 J/s.

To calculate the number of photons per second entering the eye at this intensity level, we can use the formula:

Number of photons = Power / Energy per photon

Since the wavelength is given as 500 nm, we can calculate the energy per photon using the formula:

Energy per photon = (Planck's constant * Speed of light) / Wavelength

By substituting the given values into the formula, we can calculate the energy per photon. Finally, we can use this value to calculate the number of photons per second: