(a) During laser vision correction, a brief burst of 193nm ultraviolet light is projected onto the cornea of the patient. It makes a spot 1.00mm in diameter and deposits 0.500mJ of energy. Calculate the depth of the layer ablated, assuming the corneal tissue has the same properties as water and is initially at 34.0⁰C. The tissue’s temperature is increased to 100⁰Cand evaporated without further temperature increase. (b) Does your answer imply that the shape of the cornea can be finely controlled?

Ultraviolet is a type of electromagnetic radiation with a wavelength ranging

from 10 to 400 nanometers, which is shorter than visible light but longer than X-rays.

a)

We use the following relationship to estimate heat transfer:

$$\begin{gathered} Q=mc∆+m{L}_v \\ =m\left(c∆+L_v\right) \end{gathered}$$

Rearrangeandsolveforthemassofablatedtissue:

$$\begin{gathered} m=\frac{Q}{c∆+L_v} \\ =\frac{0.5\times {10}^{-3}J}{4.186\times {10}^{3}J/kg\times C\times \left({100}^{\circ }C-{34}^{\circ }C\right)+2.256\times {10}^{6}J/kg} \\ =1.975\times {10}^{-10}kg \end{gathered}$$

Tocalculatethedensity,weusethefollowingformula:

$$\begin{gathered} \rho =\frac{m}{V} \\ =\frac{m}{\tau \tau r^{2}d} \end{gathered}$$

Rearrange and solve for the ablated layer's depth d:

role="math" localid="1654351644776" $$\begin{gathered} d=\frac{m}{\tau \tau r^2\rho } \\ =\frac{1.975\times {10}^{-10}kg}{\tau \tau \times {\left(0.5\times {10}^{-3}m\right)}^2\times 1\times {10}^{3}kg/m^3} \\ =2.515\times {10}^{-7}m \end{gathered}$$

Therefore, the laser's burst can ablate the corneal tissue to a depth of $2.515\times {10}^{-7}m$.

b)

There is a formula called the Munnerlyn formula that may be used to

calculate the thickness of cornea tissue that has to be ablated in order

to accomplish a desired change in the cornea's refractive power.

This thickness is determined by the excimer laser's ablation zone (diameter)

(an UV laser device used for eye-vision correction - which is the same as

the given problem because the wavelength of the used laser in the problem

is in the UV range) - if the ablation spot was 1.0 mm,

then a depth of $0.333\mu m$is required to achieve a change of 1.0 diopter in the

cornea's refractive power. So, it appears that the supplied laser burst can

correct vision that requires at least 0.8 diopter of correction; if the change

in refraction power is less than 0.8 diopter, the laser burst will overcorrect

the patient's vision. Another option is to expand the ablation zone;

generally, the ablation zone varies from 6 to 6.5 mm ,

if an ablation zone of 3.00 mm is chosen; however,

the ablation zone choice is restricted by the corneal thickness,

which ranges from 540 to 550 microns.

Therefore, the needed depth to be ablated in order to create a

change of 1 diopter in the cornea's refractive power

would be $3\mu m$which suggests that if the ablation zone is changeable;

the eyesight may be finely adjusted with such a laser.