Images from Lenses

Just as mirrors can form an image, lenses form images. Similar to mirrors, tracing rays works well to find image locations, but with slightly modified rules.

For converging lenses:

• Rays parallel to the optical axis will pass through the focal point on the opposite side of the lens
• Rays passing through the optical axis will pass through undeflected
• Rays passing through the focal point, or coming on a line coming through the focal point, on the same side as the object will emerge parallel to the optical axis
• If the object is farther than the focal point, the image is real and inverted
• If the object is nearer than the focal point, the image is virtual and upright
• Acts like a concave mirror

For diverging lenses:

• Rays parallel to the optical axis will appear to come from the focal point on the same side as the object
• Rays passing through the optical axis will pass through undeflected
• Rays directed at the focal point on the opposite side of the object will emerge parallel to the optical axis
• The image is always virtual and upright
• Acts like convex mirror

Equations

$$\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f},m=-\frac{d_i}{d_o}$$

• $f$ is positive for a converging lens: $f>0$.
• $f$ is negative for a diverging lens: $f<0$.
• $d_o$ is the distance to the object and is positive for a real object: $d_o>0$.
• $d_i$ is the distance to the image and is:
  • positive for a real image ($d_i>0$, opposite side of the lens from the object),
  • negative for a virtual image ($d_i<0$, same side of the lens as the object).

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