# 8.3 The electromagnetic spectrum  (Page 8/33)

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Living things—plants and animals—have evolved to utilize and respond to parts of the electromagnetic spectrum they are embedded in. Visible light is the most predominant and we enjoy the beauty of nature through visible light. Plants are more selective. Photosynthesis makes use of parts of the visible spectrum to make sugars.

## Integrated concept problem: correcting vision with lasers

During laser vision correction, a brief burst of 193-nm ultraviolet light is projected onto the cornea of a patient. It makes a spot 0.80 mm in diameter and evaporates a layer of cornea $0\text{.}\text{30}\phantom{\rule{0.25em}{0ex}}\mu \text{m}$ thick. Calculate the energy absorbed, assuming the corneal tissue has the same properties as water; it is initially at $\text{34º}\text{C}$ . Assume the evaporated tissue leaves at a temperature of $\text{100º}\text{C}$ .

Strategy

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.

Solution

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

$\text{Q}=\text{mc}\Delta T,$

where Q is the heat required to raise the temperature, $\Delta T$ 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

$Q=m\left(\text{4186 J/kg/K}\right)\left(\text{100º}\text{C}–\text{34º}\text{C}\right)=m\left(\text{276,276 J/kg}\right)=m\left(\text{276 kJ/kg}\right).$

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

${Q}_{\text{v}}={\mathrm{mL}}_{\text{v}}=m\left(\text{2256 kJ/kg}\right).$

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,

$\begin{array}{lll}m& =& \rho \text{V}\\ & =& {\text{(1000 kg/m}}^{3}\right)\left(\text{area}×\text{thickness}{\text{(m}}^{3}\text{))}\\ & =& \text{(1000 kg/}{\text{m}}^{3}\right)\left(\pi \left(0.80×{\text{10}}^{–3}\phantom{\rule{0.25em}{0ex}}\text{m}{\right)}^{2}/4\right)\left(0\text{.}\text{30}×{\text{10}}^{–6}\phantom{\rule{0.25em}{0ex}}\text{m}\right)\\ & =& 0.151×{\text{10}}^{–9}\phantom{\rule{0.25em}{0ex}}\text{kg.}\end{array}$

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

${\text{Q}}_{\text{tot}}=m\left(c\Delta \text{T}+{\text{L}}_{\text{v}}\right)=\left(0.151×{\text{10}}^{-9}\phantom{\rule{0.25em}{0ex}}\text{kg}\right)\left(\text{276 kJ/kg}+\text{2256 kJ/kg}\right)=\text{382}×{\text{10}}^{-9}\phantom{\rule{0.25em}{0ex}}\text{kJ}.$

Discussion

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 ${\text{Q}}_{\text{tot}}×\text{400}=\text{150 mW}$ .

Optics is the study of the behavior of visible light and other forms of electromagnetic waves. Optics falls into two distinct categories. When electromagnetic radiation, such as visible light, interacts with objects that are large compared with its wavelength, its motion can be represented by straight lines like rays. Ray optics is the study of such situations and includes lenses and mirrors.

When electromagnetic radiation interacts with objects about the same size as the wavelength or smaller, its wave nature becomes apparent. For example, observable detail is limited by the wavelength, and so visible light can never detect individual atoms, because they are so much smaller than its wavelength. Physical or wave optics is the study of such situations and includes all wave characteristics.

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