Question

The power of a physician’s eyes is 53.0 D while examining a patient. How far from her eyes is the feature being examined?

Short answer

The feature is 33.3 cm from the physician's eyes.

Step-by-step solution

Definition of dioptre lens

The unit of measurement for the optical power of a lens or curved mirror is the dioptre of power of a lens, which is equal to the reciprocal of focal length.

Given information and Formula to be used

Power of the physician’s eyes P = 53.0 D.

The lens-to-retina distance is, $d_i=2.00cm\left(\frac{1m}{100cm}\right)=0.02m$.

How far from her eyes is the feature being examined

The power of the eyes of a normal person can be calculated as,

$$\begin{gathered} P=\left(\frac{1}{d_{\circ }}+\frac{1}{d_i}\right) \\ 53.0D=\left(\frac{1}{0.02m}\right)+\frac{1}{d_{\circ }} \\ \frac{1}{d_{\circ }}=3.0D \end{gathered}$$

Substituting data values in the above expression gives,

$$\begin{gathered} d_{\circ }=\frac{1}{3.0D}\left(\frac{1D}{1m^{-1}}\right) \\ =0.334m\left(\frac{100cm}{1m}\right) \\ =33.4cm \end{gathered}$$

Therefore, the feature is 33.3 cm from the physician's eyes.