Question

A magnifier has a magnification of $5x$. How far from the lens should an object be held so that its image is seen at the near-point distance of $25cm$? Assume that your is immediately behind the lens.

Short answer

$5cm$far from the lens should an object be held so that its image is seen at the near-point distance of $25cm$.

Step-by-step solution

Given information

we have given that:

$m=5$

$D=25cm$

we need to find the distance $f$.

Simplify

Using the formula:

$m=\frac{D}{f}$

From the formula, let us find the value for $f$.

localid="1648723478061" $m=\frac{D}{f}$ (substitute value in the equation.)

localid="1648723490375" $m=\frac{25}{f}$ (multiply both sides with $f$.)

localid="1648736190470" role="math" $5f=\cancel{f}\times \frac{25}{\cancel{f}}$

localid="1648723581802" $5f=25$ (Divide both the sides by 5.)

localid="1648736050288" $\frac{\cancel{5}\times f}{\cancel{5}}=\frac{25}{5}$

localid="1648723617249" $f=5cm$.

$$\begin{gathered} m=\frac{D}{f} \\ 5-\frac{25}{f} \\ 5f-\cancel{f:} \end{gathered}$$