Answer to Question #118788 in Optics for nia

Question

You wish to create a real image with a magnification of −16 (that is an inverted image).

If you have a lens with a focal length of 15 cm, how far away should you place the object?

Answer 1

Magnification is given $m=-16$ ,which implies convex lens which forms real image.

Focal length of the lens is $f=15cm$ .

Let,$u=$ object distance, $v=$ image distance.

We also know that,

$$m=\frac{v}{u}$$

Which implies,

$$-16=\frac{v}{u}\implies v=-16u$$

By, standard notation, since, image is real, thus $v$ is positive and $u$ is always negative.

Now,

Lens formula is

$$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\\ \implies \frac{1}{-16u}-\frac{1}{u}=\frac{1}{15}\\ \implies -\frac{17}{16u}=\frac{1}{15}\implies u=-15.93cm$$

Hence, object should be placed $15.93cm$ to the left of the convex lens.