Question

A laser puts out 4.4 W of continuous power at a wavelength of 532 nm. The diameter of the laser beam is 5.1 mm

If the laser is pointed toward a pinhole with a diameter of 1.0 mm, how many photons travel through the pinhole per second? Assume that the light intensity is equally distributed throughout the entire cross-divisional area of the beam. (1 W = 1 J/s)

Answer 1

Solution :-

Laser put 4.4 W at 532 nm (5.32*10^-7 m)

Diameter of laser beam = 5.1 mm

Diameter of pinhole = 1.0 mm

Lets first calculate the energy of the laser beam

E= hc/wavelength

E= 6.626*10^-34 J.s * 3*10^8 m/s / 5.32*10^-7 m

E= 3.74*10^-19 J

Now using the energy of the photon we can find the number of photons

4.4 W * 1 J/s / 1 W = 4.4 J/s

Number of photons given by laser beam

4.4 J/s / 3.74*10^-19 J = 1.18*10^19 photons/s

Now lets find the ratio of the area of pinhole to area of laser beam

Area= pi* r^2

Radius of laser beam = 5.1 mm / 2 = 2.55 mm

Radius of the pinhole = 1.0 mm / 2 = 0.50 mm

Area of pinhole / area of laser beam = (pi* r^2)pinhole /(pi* r^2)laser beam

                                                                  = (3.14*(0.50mm)^2)/(3.14*(2.55mm)^2)

                                                                  = 0.03845

Now lets calculate the number of photons travel through the pinhole

Number of photons travel through pinhole = 0.03845 * 1.18*10^19 photon/s = 4.54*10^17 photons/s

Hence the answer is 4.54*10^17 photon/s will travel through the pinhole