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Lenses and Mirrors
Ray Diagrams, Focal Points, and Image Formation
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Lenses and mirrors control the path of light to form images. A converging (convex) lens bends light rays toward a focal point; a diverging (concave) lens bends them outward. Concave mirrors focus parallel rays to a point; convex mirrors spread them. The image formed can be real or virtual, upright or inverted, magnified or reduced - and the thin lens equation plus sign conventions let you predict exactly which.
Ray diagrams are the standard tool for analyzing optical systems. Three principal rays for a lens (parallel to axis, through focal point, through center) always converge at the image location. Practicing ray diagrams by hand builds intuition before plugging numbers into formulas.
Key Facts
- Thin lens/mirror equation: 1/f = 1/d_o + 1/d_i
- Magnification:
- Real images form on the opposite side of a lens from the object (same side for mirrors); virtual images do not.
- Converging lens: positive focal length. Diverging lens: negative focal length.
- Object beyond 2f: image is real, inverted, smaller. Object between f and 2f: image is real, inverted, larger.
- Object inside f (converging lens): virtual, upright, magnified image on same side as object.
Vocabulary
- Focal length (f)
- Distance from the lens or mirror to the focal point; positive for converging, negative for diverging.
- Real image
- An image formed where light rays actually converge; can be projected onto a screen.
- Virtual image
- An image formed where light rays appear to diverge from; cannot be projected onto a screen.
- Magnification
- Ratio of image height to object height. Positive = upright; negative = inverted.
- Focal point
- The point at which parallel rays converge after passing through a converging lens or reflecting from a concave mirror.
Common Mistakes to Avoid
- Using the wrong sign convention. Commit to one system (e.g. real is positive) and apply it consistently for all distances.
- Forgetting that a virtual image is upright. When m is positive, the image is upright - even if it's on the same side as the object.
- Assuming all mirrors/lenses produce the same kind of image. The object distance relative to f completely determines image type.
- Drawing ray diagrams with incorrect principal rays. The three standard rays must be drawn to the lens plane first before refracting.
Practice Questions
- 1 An object is placed 30 cm from a converging lens with f = 10 cm. Find the image distance and describe the image.
- 2 A diverging lens has f = -20 cm. Where is the image of an object 40 cm from the lens?
- 3 Use a ray diagram to show what happens when an object is placed inside the focal point of a magnifying glass.