Three Magic Rays
The only three rays you ever need to draw
What this lesson covers
Why it matters
Millions of rays leave every point of an object. To find the image, you only ever need to draw TWO of three special ones — they do all the work.
The idea in plain words
Your exam toolkit. Tap each ray.
ray ① ∥ axis → F · ray ② through O · ray ③ through F → ∥ axis
Object beyond 2F of a convex lens. Use rays ① and ② to locate the image.
Image: between F and 2F, real, inverted, diminished
- construction ray: ① — comes in parallel to the axis, leaves through the far focus F
- construction ray: ② — aims at the optical centre O, passes dead straight
- construction ray: ③ — passes through the near focus F first, leaves parallel to the axis
- ① from the tip, parallel, bends through F
- ② from the tip through O, straight
- They cross between F and 2F on the other side
Predict first
A ray passes exactly through the optical centre of a thin lens. It…
At the centre the two faces are parallel — like a thin slab — so the ray goes straight. That's magic ray ②.
- continues straight, undeviated — correct
- bends through the focus
- reflects back
What you do
Build the ray diagram: add each of the three construction rays and watch them all pin the SAME image point.
Check yourself
Why do we draw only two rays when millions exist?
The lens focuses every ray from a point to the same image point; the special two are just the easiest to draw.
Ray ③ (through the focus first) emerges…
Ray ③ is ray ① played backwards — light paths are reversible.
If the top half of the lens is covered, the image…
Every part of the lens forms the WHOLE image — rays through the open half still converge to every image point, only fewer of them.
- ALL rays from that point meet at the image — two are enough to find where — correct
- lenses only pass two rays
- the others are too weak
- parallel to the principal axis — correct
- through the other focus
- undeviated
- stays complete, just dimmer — correct
- loses its top half
- disappears