Question

A thin lens of focal length 12.5 cm has a 5.0 cm tall object placed 10 cm in front of it. Where will the image be formed?

Answer 1

Concepts and reason

The concepts used to solve this problem are focal length, image distance, and object distance.

Initially, use the thin lens equation to determine the relationship between the focal length, image distance, and object distance.

Finally, use the focal length and object distance to determine the image distance of the lens.

Fundamentals

The expression for thin lens formula is as follows:

\(\frac{1}{f}=\frac{1}{i}+\frac{1}{o}\)

Here, the focal length is f, the image distance is i, and the object distance is o.

The lens's focal length is when the initial parallel rays to the lens are brought to focus on the principal axis of the lens.

The expression for the focal length is as follows:

\(\frac{1}{f}=\frac{1}{i}+\frac{1}{o}\)

Rearrange the above expression.

$$ \begin{aligned} \frac{1}{i} &=\frac{1}{f}-\frac{1}{o} \\ &=\frac{o-f}{f(o)} \end{aligned} $$

Simplify the above expression for image distance.

$$ i=\frac{f(o)}{o-f} $$

The expression for the image distance is,

$$ i=\frac{f(o)}{o-f} $$

Substitute for f and for.

$$ \begin{aligned} i &=\frac{(12.5 \mathrm{~cm})(10 \mathrm{~cm})}{(10 \mathrm{~cm}-12.5 \mathrm{~cm})} \\ &=\frac{125 \mathrm{~cm}}{-2.5 \mathrm{~cm}} \\ &=-50 \mathrm{~cm} \end{aligned} $$