Suppose that you have a 10 Watt green LED lamp, that emits light at a wavelength of 535 nm uniformly in all directions. 1) Suppose that you look at the lamp from a distance of 3 meters. If your face has an area of 175 cm2 facing the LED, how many photons from the lamp hit your face each second?

Each second approximately photons hit the face

Explanation:

Emmited intensity of electromagentic waves is defined as:

(1)

with P the power and A_{wave-front} the surface of the sphere that defines the wave front at a given radial distance (r) from the source, this is:

(2)

Using (2) on (1):

That is the intensity of ligth at 3 meters from the source so that it's the intensity the face absorbs so again using equation (1) but now for absorbed intensity:

(3)

Power is the energy over a perioid of time this is:

(4)

But energy of photons is:

(5)

with n the number of photons, h Planck's constant,c velocity odf ligth and the wavelength

Using (5) on (4) and (4) on (3):

Solving for n