Overview
This lecture covers how to draw ray diagrams for concave (diverging) and convex (converging) lenses, including image characteristics in various scenarios.
Concave (Diverging) Lenses
- Concave lenses make light rays spread out (diverge).
- Diagram symbol: lens with outward V shapes at both ends.
- Draw a horizontal axis through the lens center and mark focal points (F) on both sides.
- Mark 2F points, twice as far from lens as F; mainly used for convex lenses.
- To draw rays: one from the object parallel to the axis, the other through the lens center (not refracted).
- The parallel ray is refracted away from the lens, appearing to come from F (use dashed line from F to lens).
- Image position is where the extrapolated rays cross; for an object on the axis, the image base is also on the axis.
- Image is always virtual (cannot be projected), upright, and smaller than the object.
Convex (Converging) Lenses
- Convex lenses focus light rays to a single point (converge).
- Diagram symbol: lens with inward V shapes at both ends.
- Draw axis, focal points (F), 2F points, object, and two incident rays.
- One ray passes straight through the lens center (not refracted), the other runs parallel to the axis and refracts through F on the opposite side.
- Image forms where the refracted rays cross.
- For objects more than 2F from lens: image is real (can be projected), inverted (upside down), and smaller than object.
- At 2F: image is real, inverted, and the same size as the object.
- Between F and 2F: image is real, inverted, and larger than the object.
- If object is between F and the lens: rays diverge, use dashed lines to trace back; image is virtual, upright, and larger than object.
- Always draw rays from the top of the object (e.g., arrow's tip).
Key Terms & Definitions
- Concave lens — a lens that diverges light rays; thicker at the edges.
- Convex lens — a lens that converges light rays; thicker at the center.
- Focal point (F) — point where rays either converge (convex) or appear to diverge from (concave) after passing through the lens.
- 2F — a point twice the distance from the lens as F, used for determining image properties.
- Virtual image — cannot be projected; formed by apparent divergence of rays.
- Real image — can be projected; formed where refracted rays actually converge.
- Inverted — image is upside down compared to the object.
Action Items / Next Steps
- Practice drawing ray diagrams for concave and convex lenses with different object positions.
- Review definitions and image characteristics for exam revision.