Chapter 37, Problem 1PQ

A camera obscura is used to form an image of a distant object. If the object is 10.0 m away from the aperture and the magnification of the image is –0.15, what is the image distance?

To determine

The distance of the image.

Answer to Problem 1PQ

The image distance is $1.5\text{m}$.

Explanation of Solution

Write the expression for the magnification.

    $M=-\frac{d_{\text{i}}}{d_0}$

Here, $M$ is the magnification, $d_{\text{i}}$ is the distance of the image from pinhole, $d_0$ is the object distance from pinhole.

From the above equation we get,

    $d_{\text{i}}=-d_{0}M$                                                                                                                (I)

Conclusion:

Substitute $10.0\text{m}$ for $d_{\text{o}}$ and $-0.15$ for $M$. in equation (I) to get $d_{\text{i}}$.

    $\begin{array}{c}{d}_{\text{i}}=-\left(10.0\text{m}\right)\left(-0.15\right)\\ =1.5\text{m}\end{array}$

Therefore, the image distance is $1.5\text{m}$.