Question

the average threshold of dark-adapted (scotopic) vision is 4.00 10-11 w/m2 at a central wavelength of 500 nm. if light with this intensity and wavelength enters the eye and the pupil is open to its maximum diameter of 8.00 mm, how many photons per second enter the eye?

Answer 1

The number of photons per second entering the eye can be calculated by finding the power incident on the eye and dividing it by the energy carried by each photon.

Calculating this value gives us approximately 3.8 × 1018 photons per second entering the eye.

Step-by-step explanation:

To calculate the number of photons per second entering the eye, we need to calculate the power incident on the eye first. Using the given average threshold of dark-adapted vision and the maximum diameter of the pupil, we can calculate the power incident on the eye.

Power = Intensity × Area
Intensity = 4.00 × 10-11 W/m2
Area = π(0.008 m)2 = 6.28 × 10-5 m2

Plugging in these values, we get:
Power = (4.00 × 10-11 W/m2) × (6.28 × 10-5 m2) = 2.51 × 10-15 W

Since each photon carries an energy of E = hf, where h is Planck's constant (6.63 × 10-34 Js) and f is the frequency, we can calculate the number of photons per second using:
Number of photons per second = Power / E
Number of photons per second = (2.51 × 10-15 W) / (6.63 × 10-34 Js)

Calculating this value gives us approximately 3.8 × 1018 photons per second entering the eye.

Answer 2

The intensity of the light is 4.00 x 10-11 W/m2 at a wavelength of 500 nm, and the maximum pupil diameter is 8.00 mm. By calculating the energy per second and the energy per photon, we can determine that approximately 2.53 x 103 photons per second enter the eye.

Step-by-step explanation:

To calculate the number of photons per second that enter the eye, we need to consider the intensity of the light, the wavelength, and the diameter of the pupil. The intensity of the light is given as 4.00 x 10-11 W/m2 and the wavelength is 500 nm. The maximum diameter of the pupil is 8.00 mm.

To calculate the number of photons, we need to convert the intensity into energy per second using the formula:

Energy = Intensity x Area = Intensity x πr2

where r is the radius of the pupil. In this case, r = 8.00 mm / 2 = 4.00 mm = 4.00 x 10-3 m.

Substituting the values into the formula, we get:

Energy = (4.00 x 10-11 W/m2) x π(4.00 x 10-3)2 m2

Simplifying the equation gives:

Energy = 1.01 x 10-15 J/s

Next, we need to calculate the energy per photon using the formula:

Energy per Photon = Planck's Constant x Speed of Light / Wavelength

Substituting the values gives:

Energy per Photon = (6.63 x 10-34 J.s) x (3.00 x 108 m/s) / (500 x 10-9 m)

Simplifying the equation gives:

Energy per Photon = 3.98 x 10-19 J

Finally, we can calculate the number of photons per second using the formula:

Number of Photons = Energy / Energy per Photon

Substituting the values gives:

Number of Photons = (1.01 x 10-15 J/s) / (3.98 x 10-19 J)

Simplifying the equation gives:

Number of Photons = 2.53 x 103 photons/s