91Ó°ÊÓ

When $y$ varies inversely as $x$ then it is known as an inverse variation.

Relationship of the form $xy=k$ or $y=\frac{k}{x}$where $x,y≠0$ for some nonzero constant $k$ is known as inverse variation. Here $P=\frac{1}{f}$ that is., $Pf=1$, clearly when compared with $xy=k$ it can be observed that the equation is an inverse variation with $k=1$.

The graph of inverse variation $P=\frac{1}{f}$is given by:

Relationship of the form $xy=k$ or $y=\frac{k}{x}$where role="math" localid="1648107671616" $x,y≠0$ for some nonzero constant $k$ is known as inverse variation i.e., $y$ varies inversely as $x$.

Substitute 0.2 for $f$into the formula $P=\frac{1}{f}$and simplify for $P$.

$$\begin{gathered} P=\frac{1}{f} \\ =\frac{1}{0.2} \\ =\frac{10}{2} \\ =5 \end{gathered}$$

Substitute $-0.4$ for f into the formula $P=\frac{1}{f}$and simplify for $P$.

$P=\frac{1}{f}$

$=−\frac{1}{0.4}$

$=−\frac{10}{4}$

$=−2.5$

Therefore, the power of the lens with $+0.2$focal length is $+5$diopters and the power of the lens with $-0.4$focal length is $-2.5$diopters.