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The minimum light intensity that the human eye can perceive is 10-10 Wm-2. The area of the opening of our eye (the pupil) is approximately 4 cm-2. Consider yellow light with wavelength λ = 600 nm. The number of photons incident on the retina per second at the minimum intensity for the eye to respond is
- a)1.5 × 103
- b)5 × 103
- c)8 × 103
- d)1.2 × 104
Correct answer is option 'D'. Can you explain this answer?
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Given:
Minimum light intensity: 10^-10 Wm^-2
Area of the pupil: 4 cm^2 = 4 x 10^-4 m^2
Wavelength of yellow light: 600 nm = 600 x 10^-9 m
To find:
Number of photons incident on the retina per second at the minimum intensity for the eye to respond.
Solution:
Step 1: Convert the intensity to photons per second
The energy of a single photon can be calculated using the equation:
E = hc/λ
where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 Js), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength of the light.
Using this equation, we can calculate the energy of a single photon of yellow light:
E = (6.626 x 10^-34 Js)(3 x 10^8 m/s) / (600 x 10^-9 m)
E ≈ 3.313 x 10^-19 J
The number of photons per second can be calculated by dividing the intensity by the energy of a single photon:
Number of photons per second = Intensity / Energy of a single photon
Intensity = 10^-10 Wm^-2
Number of photons per second = (10^-10 Wm^-2) / (3.313 x 10^-19 J)
Step 2: Convert the area of the pupil to meters squared
The area of the pupil is given as 4 cm^2. To convert it to meters squared, we divide by 10,000:
Area of the pupil = 4 x 10^-4 m^2
Step 3: Calculate the number of photons incident on the retina per second
The total number of photons incident on the retina per second can be calculated by multiplying the number of photons per second by the area of the pupil:
Total number of photons incident on the retina per second = Number of photons per second x Area of the pupil
Total number of photons incident on the retina per second = (10^-10 Wm^-2) / (3.313 x 10^-19 J) x (4 x 10^-4 m^2)
Total number of photons incident on the retina per second ≈ 1.2 x 10^4
Therefore, the number of photons incident on the retina per second at the minimum intensity for the eye to respond is approximately 1.2 x 10^4, which corresponds to option 'D'.
Minimum light intensity: 10^-10 Wm^-2
Area of the pupil: 4 cm^2 = 4 x 10^-4 m^2
Wavelength of yellow light: 600 nm = 600 x 10^-9 m
To find:
Number of photons incident on the retina per second at the minimum intensity for the eye to respond.
Solution:
Step 1: Convert the intensity to photons per second
The energy of a single photon can be calculated using the equation:
E = hc/λ
where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 Js), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength of the light.
Using this equation, we can calculate the energy of a single photon of yellow light:
E = (6.626 x 10^-34 Js)(3 x 10^8 m/s) / (600 x 10^-9 m)
E ≈ 3.313 x 10^-19 J
The number of photons per second can be calculated by dividing the intensity by the energy of a single photon:
Number of photons per second = Intensity / Energy of a single photon
Intensity = 10^-10 Wm^-2
Number of photons per second = (10^-10 Wm^-2) / (3.313 x 10^-19 J)
Step 2: Convert the area of the pupil to meters squared
The area of the pupil is given as 4 cm^2. To convert it to meters squared, we divide by 10,000:
Area of the pupil = 4 x 10^-4 m^2
Step 3: Calculate the number of photons incident on the retina per second
The total number of photons incident on the retina per second can be calculated by multiplying the number of photons per second by the area of the pupil:
Total number of photons incident on the retina per second = Number of photons per second x Area of the pupil
Total number of photons incident on the retina per second = (10^-10 Wm^-2) / (3.313 x 10^-19 J) x (4 x 10^-4 m^2)
Total number of photons incident on the retina per second ≈ 1.2 x 10^4
Therefore, the number of photons incident on the retina per second at the minimum intensity for the eye to respond is approximately 1.2 x 10^4, which corresponds to option 'D'.
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The minimum light intensity that the human eye can perceive is 10-10 Wm-2. The area of the opening of our eye (the pupil) is approximately 4 cm-2. Consider yellow light with wavelength = 600 nm. The number of photons incident on the retina per second at the minimum intensity for the eye to respond isa)1.5 103b)5 103c)8 103d)1.2 104Correct answer is option 'D'. Can you explain this answer?
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