Intensity of the HeNe laser (lambda = 632nm) was measured at 2 distances: 1m and 200m from the laser. The meter reading was 10W and 1W correspondingly. How many photons/sec will enter your eye if you look into the laser from 1m? From 2m? Assume that radius of the pupil was 2.4mm, radius of the detector was 3.5mm. At a distance of 1m the laser beam radius was 1mm.

Question

Intensity of the HeNe laser (lambda = 632nm) was measured at 2 distances: 1m and 200m from the laser. The meter reading was 10W and 1W correspondingly. How many photons/sec will enter your eye if you look into the laser from 1m? From 2m? Assume that radius of the pupil was 2.4mm, radius of the detector was 3.5mm. At a distance of 1m the laser beam radius was 1mm.

Answer 1

To calculate the number of photons entering your eye when looking into the laser, we need to use the formula:

Number of photons = (Power / Energy per photon)

First, let's calculate the energy per photon using the equation:

Energy per photon (E) = Planck's constant (h) * speed of light (c) / wavelength

Given that the wavelength of the HeNe laser is λ = 632 nm = 632 × 10^(-9) m, we can substitute the values:

E = (6.626 × 10^(-34) J s) * (3 × 10^8 m/s) / (632 × 10^(-9) m)

E = 3.135 × 10^(-19) J

Now let's calculate the number of photons entering your eye from a distance of 1m:

Power at 1m = 10W

Number of photons at 1m = (10W / 3.135 × 10^(-19) J)

Number of photons at 1m = 3.19 × 10^19 photons/sec

Next, let's calculate the number of photons entering your eye from a distance of 200m. At this distance, we need to account for the spreading of the laser beam.

Given that the laser beam radius at 1m is 1mm = 0.001m, we can calculate the beam area at that distance:

Beam Area at 1m = π * (Beam radius at 1m)^2

Beam Area at 1m = π * (0.001m)^2

Beam Area at 1m = 3.14 × 10^(-6) m^2

Now let's calculate the beam area at 200m. Since the beam diverges, we can use the formula:

Beam radius at 200m = Beam radius at 1m * (Distance at 200m / Distance at 1m)

Beam radius at 200m = 0.001m * (200m / 1m)

Beam radius at 200m = 0.2m

Beam Area at 200m = π * (0.2m)^2

Beam Area at 200m = 0.1256 m^2

Now, let's calculate the power at 200m using the power at 1m and the beam area change:

Power at 200m = (Power at 1m) * (Beam Area at 1m / Beam Area at 200m)

Power at 200m = 10W * (3.14 × 10^(-6) m^2 / 0.1256 m^2)

Power at 200m = 0.2516W

Finally, let's calculate the number of photons entering your eye from a distance of 200m:

Number of photons at 200m = (0.2516W / 3.135 × 10^(-19) J)

Number of photons at 200m = 8.01 × 10^17 photons/sec

So, the number of photons entering your eye from a distance of 1m is approximately 3.19 × 10^19 photons/sec, and from a distance of 200m is approximately 8.01 × 10^17 photons/sec.