Integrated Concept Problem: Correcting Vision with Lasers

The energy from the laser light goes toward raising the temperature of the tissue and also toward evaporating it. Thus we have two amounts of heat to add together. Also, we need to find the mass of corneal tissue involved.

To figure out the heat required to raise the temperature of the tissue to $\text{100º}\text{C}$, we can apply concepts of thermal energy. We know that

where Q is the heat required to raise the temperature, $\mathrm{\Delta }T$ is the desired change in temperature, $m$ is the mass of tissue to be heated, and $c$ is the specific heat of water equal to 4186 J/kg/K.

Without knowing the mass $m$ at this point, we have

The latent heat of vaporization of water is 2256 kJ/kg, so that the energy needed to evaporate mass $m$ is

To find the mass $m$, we use the equation $\rho =m/\text{V}$, where $\rho$ is the density of the tissue and $\text{V}$ is its volume. For this case,

Therefore, the total energy absorbed by the tissue in the eye is the sum of $\text{Q}$ and ${\text{Q}}_{\text{v}}$:

The lasers used for this eye surgery are excimer lasers, whose light is well absorbed by biological tissue. They evaporate rather than burn the tissue, and can be used for precision work. Most lasers used for this type of eye surgery have an average power rating of about one watt. For our example, if we assume that each laser burst from this pulsed laser lasts for 10 ns, and there are 400 bursts per second, then the average power is ${\text{Q}}_{\text{tot}}\times \text{400}=\text{150 mW}$.