6.10 - How to Draw Ray Diagrams

Overview

This lecture explains how to draw ray diagrams for concave (diverging) and convex (converging) lenses, and how to analyze the resulting images.

Concave lenses are represented with outward "V" shapes at the ends and are thinner in the center.
The axis is a horizontal line through the lens center, with focal points (F) on both sides.
Each focal point (F) is the principal focus; 2F is twice the distance from the lens as F.
Draw one incident ray parallel to the axis from the top of the object, and one through the lens center.
The ray passing through center is not refracted; the parallel ray refracts outward as if from F.
Use dashed lines for virtual rays extending backward to F.
The image forms where the refracted and extended rays cross.
For objects on the axis, the bottom of the image is also on the axis.
Images formed by concave lenses are always virtual, upright, and smaller than the object.

Convex lenses are shown with inward "V" shapes at the ends and are thicker in the center.
Setup is similar: axis, object, focal points (F and 2F), and two incident rays.
The ray through the lens center is not refracted; the parallel ray refracts through F on the opposite side.
The image location is where the refracted rays meet.
When the object is beyond 2F, the image is real, inverted, and smaller than the object.
If the object is at 2F, the image is real, inverted, and the same size.
If the object is between F and 2F, the image is real, inverted, and larger.
If the object is between F and the lens, the image is virtual, upright, and larger; rays do not meet unless extended backward.

Concave (Diverging) Lens — A lens that spreads out light rays and forms only virtual, upright, smaller images.
Convex (Converging) Lens — A lens that brings light rays together and can form real or virtual images, depending on object position.
Principal Axis — The horizontal line passing through the center of the lens.
Focal Point (F) — The point where parallel rays converge (convex) or appear to diverge from (concave).
2F — A point twice the distance from the lens as the focal point.
Real Image — An image formed by actual intersection of light rays; can be projected onto a screen.
Virtual Image — An image formed by the apparent intersection of rays, cannot be projected.

Practice drawing ray diagrams for both lens types using simple objects like arrows.
Remember to always draw incident rays from the top of the object.
Prepare to describe the nature (real/virtual, upright/inverted, size) of images in exams.