Question

The threshold of sensitivity of the human eye is about 100 photons per second. The eye is most sensitive at a wavelength of around 550 nm. For this wavelength, determine the threshold in watts of power.

a) 1.80×10 −14W
b) 3.60×10 −14W
c) 5.40×10 −14W
d) 7.20×10 −14W

Answer 1

To determine the human eye's sensitivity threshold in watts, we calculate the energy of a single photon with a wavelength of 550 nm and then multiply by 100 photons per second. The calculation reveals that the sensitivity threshold is around 3.61 × 10-17 W, which does not match any of the provided options.

Step-by-step explanation:

The question requires calculating the threshold power sensitivity of the human eye in watts, given the sensitivity in terms of photons per second. To find the energy of one photon with a wavelength of 550 nm, we use the formula E = hc / λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength in meters. The calculation goes as follows:

• h = 6.626 × 10-34 J·s (Planck's constant)
• c = 3.00 × 108 m/s (speed of light)
• λ = 550 × 10-9 m (wavelength of light)

By substituting these values into the energy formula, we get:

E = (6.626 × 10-34 J·s × 3.00 × 108 m/s) / 550 × 10-9 m = 3.61 × 10-19 J (energy per photon)

This is the energy for one photon. Since the eye is sensitive to 100 photons per second, the threshold in terms of power (energy per time) is:

Power = 3.61 × 10-19 J/photon × 100 photons/s = 3.61 × 10-17 W

However, this does not match any of the given options, hence, there must be a mistake in the provided options or in the premise of the question. Based on the calculation with the correct constants, none of the options a), b), c), or d) is accurate.