Question

A student’s eyes, while reading the blackboard, have a power of 51.0 D. How far is the board from his eyes?

Short answer

The board is 1 m far from the student'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

The power of a student’s eye is P = 51.0 D

The lens-to-retina distance is, \({{\rm{d}}_{\rm{i}}} = {\rm{2}}{\rm{.00 cm}}\left( {\frac{{1\;{\rm{m}}}}{{100\;{\rm{cm}}}}} \right) = {\rm{0}}{\rm{.02 m}}\).

How far is the board from his eyes?

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

$$\begin{gathered} P=\left(\frac{1}{d_{\circ }}+\frac{1}{d_i}\right) \\ 51.0D=\left(\frac{1}{0.02m}+\frac{1}{d_{\circ }}\right) \\ 51.0D=51.0D+\frac{1}{d_{\circ }} \\ \frac{1}{d_{\circ }}=1.0D \end{gathered}$$

This result in the value of

$$\begin{gathered} \frac{1}{d_{\circ }}=1.0D\left(\frac{1m^{-1}}{1D}\right) \\ {d}_{\circ }=1m \end{gathered}$$

Therefore, the board is 1 m from the student's eyes.