Lateral magnification \( m \) is the ratio of image height \( y' \) to object height \( y \):
\[ m = \frac{y'}{y} = -\frac{v}{u} \]
- If \( m > 0 \), the image is upright.
- If \( m < 0 \), the image is inverted.
In multi-lens systems, such as microscopes and telescopes, the total magnification is the product of individual magnifications:
\[ M_{\text{total}} = M_1 \times M_2 \]
For a compound microscope, the total magnification is:
\[ M = m_{\text{objective}} \times m_{\text{eyepiece}} \]
Used for devices like magnifying glasses and telescopes. It compares the angular size of the image with and without the instrument.
\[ M = \frac{\theta'}{\theta} \]
For a simple magnifier, the magnification is approximately:
\[ M = \frac{25\ \text{cm}}{f} \]
where \( f \) is the focal length of the lens and 25 cm is the near point of a relaxed human eye.
An object is placed 12 cm in front of a convex lens, and the image is formed 36 cm on the other side. Find the magnification and describe the image.
\[ m = -\frac{v}{u} = -\frac{36}{12} = -3 \]
The magnification is -3, meaning the image is real, inverted, and 3 times larger than the object.
Written by Albert Marin