Question

(a) What is the frequency of the \(193 - nm\)ultraviolet radiation used in laser eye surgery? (b) Assuming the accuracy with which this EM radiation can ablate the cornea is directly proportional to wavelength, how much more accurate can this UV be than the shortest visible wavelength of light?

Short answer

(a) The frequency of the ultraviolet radiation used in laser eye surgery is \(1.55 \times {10^{15}}\;Hz\).

(b) The accuracy of given UV radiation is \(97\% \) more than that of the shortest

Step-by-step solution

Definition of Concept

Electric and magnetic disturbances that oscillate or electrically charged particles moving through a vacuum or material produce electromagnetic radiation, a type of energy.

Information Provided

• Wavelength of the UV radiation: \(193 - nm\)

Calculating the frequency  

(a)

Consider the given information.

The ultraviolet radiation's wavelength is\(\lambda = 193\;nm\).

Apply the formula,

The relationship between frequency and wavelength is as follows:

\(f = \frac{c}{\lambda }\)

Putting the values,

\(\begin{array}{c}f = \frac{{3 \times {{10}^8}}}{{1.93 \times {{10}^{ - 7}}}}\\ = 1.55 \times {10^{15}}\;Hz\end{array}\)

Therefore, the required frequency is \(1.55 \times {10^{15}}\;Hz\)

Find the required accuracy 

(b)

Consider the given information,

The ultraviolet radiation's wavelength is\(\lambda = 193\;nm\).

Apply the formula,

The wavelength has a direct relationship to the accuracy.

Accuracy \(\mu \lambda \)

The shortest visible light wavelength is \({\lambda _{visible{\rm{ }}}} = 380\;nm\). Then,

\(\begin{array}{c}\frac{{{\lambda _{visthle{\rm{ }}}}}}{{{\lambda _{UV}}}} = \frac{{380}}{{193}}\\ = 1.97\end{array}\)

Therefore, the accuracy of given UV radiation is about \(97\% \) .