The largest average laser light intensity that the retina of the eye can tolerat

Question

The largest average laser light intensity that the retina of the eye can tolerate without being damaged (damage threshold) is I_ove = l.0times10^2 W/m^2. What is the largest average power that a laser beam of 1.5 mm in diameter can have and still be safe to the retina? How much energy would this beam deliver per second to the retina? What are the maximum values of the electric and magnetic fields for this beam? If the wavelength of this laser light is 680 nm, figure out the electric and magnetic field vectors as a function of time and space. (Assume E is along y and B is along z direction.) What is the Poynting vector for this EM wave? If this laser light was not a beam of light, but a spherically symmetric radiation, then how much energy would escape a window of area 4.5 cm^2 per second 1.2 m away? What is the maximum E and B filed strenghts at this point?

Explanation / Answer

A. S = P/A

P = S*A

P = (1*10^2 W/m^2)*(3.14*1.5^2*10^-6/4 m^2)

P = 1.76*10^-4 W

B.

U = P*t

U= 1.76*10^-4 W * 1 sec

U = 1.76*10^-4 J

C.

S = c*E^2/8*pi*k

E = sqrt(8*pi*k*S/c)

E = sqrt(8*3.14*9*10^9*10^2/(3*10^8))

E = 274.51 N/C

Bmax = Emax/c

Bmax = 274.51/(3*10^8)

Bmax = 9.15*10^-7 Wb

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