How do I know if a lens or mirror will form a magnified or diminished image?

You can determine this using the magnification formula. For both mirrors and lenses, magnification ($m$) is defined as the ratio of the height of the image ($h'$) to the height of the object ($h$), i.e., $m = \frac{h'}{h}$. It can also be related to object distance ($u$) and image distance ($v$). For mirrors, $m = -\frac{v}{u}$, and for lenses, $m = \frac{v}{u}$.

• If the absolute value of magnification, $|m|$, is greater than 1 ($|m| > 1$), the image is magnified.
• If $|m|$ is less than 1 ($|m| < 1$), the image is diminished.
• If $|m|$ is equal to 1 ($|m| = 1$), the image is of the same size as the object. Additionally, if $m$ is positive, the image is erect; if $m$ is negative, the image is inverted.