gen-define-the-thin-lens-equation-and-give-one-short-worked-exam-17f4

Define the thin-lens equation and give one short worked example.

# Thin-Lens Equation The thin-lens equation relates the object distance, image distance, and focal length of a thin lens: $$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$ Where: - **f** = focal length of the lens - **d_o** = object distance (from lens to object) - **d_i** = image distance (from lens to image) **Sign conventions:** - f is positive for converging (convex) lenses, negative for diverging (concave) lenses - d_o is positive for real objects (on the incoming light side) - d_i is positive for real images, negative for virtual images ## Worked Example **Problem:** An object is placed 30 cm in front of a converging lens with focal length 10 cm. Where is the image formed? **Solution:** Given: d_o = 30 cm, f = 10 cm $$\frac{1}{d_i} = \frac{1}{f} - \frac{1}{d_o}$$ $$\frac{1}{d_i} = \frac{1}{10} - \frac{1}{30} = \frac{3-1}{30} = \frac{2}{30}$$ $$d_i = 15 \text{ cm}$$ The image forms **15 cm behind the lens** (positive value = real image).