Question

An object is placed 10 cm from a convex lens of focal length 20 cm. What is the magnification?

A. 1.0

B. 2.0

C. 1.5

D. 2.5

E. .50

Answer 1

Concepts and reason

The concepts used to solve the given problem are based on convex lens and the magnification of convex lens.

Use the equation for the convex lens to calculate the image distance from the lens. Next, use the expression for the magnification of the convex lens and substitute the necessary values to calculate the magnification of the given lens.

Fundamentals

The equation for the convex lens is,

$\frac{1}{f} = \frac{1}{p} + \frac{1}{q}$

Here, $q$ is the image distance from the convex lens, $f$ is the focal length of the convex lens, and $p$ is the object distance from the convex lens.

The expression for the magnification of the convex lens is,

$m = - \frac{q}{p}$

Here, m is the value of the magnification of the convex lens.

Write the value of the object distance from the convex lens.

$p = 10{\rm{ cm}}$

Write the value of the focal length of the convex lens.

$f = 20{\rm{ cm}}$

Write the equation for the convex lens.

$\frac{1}{f} = \frac{1}{p} + \frac{1}{q}$

Rearrange for $q$ .

$q = \frac{{fp}}{{p - q}}$

Substitute $10{\rm{ cm}}$ for $p$ and $20{\rm{ cm}}$ for $f$ .

$\begin{array}{c}\\q = \frac{{\left( {20{\rm{ cm}}} \right)\left( {10{\rm{ cm}}} \right)}}{{10{\rm{ cm}} - 20{\rm{ cm}}}}\\\\ = - \frac{{200{\rm{ cm}}}}{{10}}\\\\ = - 20{\rm{ cm}}\\\end{array}$

Write the expression for the magnification of the convex lens.

$m = - \frac{q}{p}$

Substitute $\left( { - 20{\rm{ cm}}} \right)$ for $q$ and $10{\rm{ cm}}$ for $p$ .

$\begin{array}{c}\\m = - \frac{{\left( { - 20{\rm{ cm}}} \right)}}{{10{\rm{ cm}}}}\\\\ = 2\\\end{array}$

Ans:

The value of the magnification is $2$ .