Diverging Lenses
Glasses for nearsightedness and door peepholes
Do Now: Look through the peephole in a door and the whole hallway appears, small and upright. What kind of lens is in the peephole?
A diverging lens. Like a convex mirror, it spreads light out and gives a wide, smaller, upright view.
A. The Three Principal Rays
Ray 1 — Parallel Ray
Travels parallel to the principal axis, then bends away as if it came from F on the near side (trace it back with a dashed line).
Ray 2 — Focal Ray
Aims toward F on the far side, then leaves the lens parallel.
Ray 3 — Center Ray
Goes through the center of the lens without bending.
B. The Image Is Always the Same Type
Object far from the lens — click Next to draw it step by step.
Object close to the lens — click Next to draw it step by step.
Describe the image using L-O-S-T.
L: same side as the object, between F and the lens O: upright S: smaller T: Virtual
A diverging lens behaves just like a convex mirror. The only difference: the lens’s virtual image is on the same side as the object, while the mirror’s is behind the mirror.
Explore: Diverging Lens
Drag the orange object. Turn rays on and off with the check boxes.
C. Diverging Lenses at Work
Glasses for nearsightedness: the eye focuses light too soon. A diverging lens spreads the light a little so it focuses on the retina.
Door peepholes: a wide, upright view of the hallway.
Telescopes & binoculars: some designs use a diverging eyepiece.
Laser beam expanders: spread a narrow beam before it is re-focused.
Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. A diverging lens is
2. A diverging lens always makes an image that is
3. A ray parallel to the principal axis passes through a diverging lens. It leaves the lens
4. Which vision problem is corrected with diverging lenses?
5. Which mirror forms images like a diverging lens does?
Glasses for Nearsightedness
A nearsighted person’s eye focuses light from distant objects in front of the retina, so distant objects look blurry. An eye doctor prescribes eyeglasses with diverging lenses.
How does a diverging lens help a nearsighted eye?
▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)
Challenge score: 0 / 6
C1. What kind of image does a single diverging lens always form of a real object?
C2. A diverging lens has a focal length of −15 cm (the negative sign shows a virtual focal point). A 6.0-cm-tall object is placed 30. cm from the lens. Substitute numerical values into a mathematical representation that can be used to determine the image distance. Then calculate it.
C3. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response.
C4. For the 6.0-cm-tall object 30. cm from the diverging lens, the image forms 10. cm from the lens on the object’s side. Determine the height of the image.
C5. A ray parallel to the axis passes through a diverging lens. Where does it go?
C6. A hiker tries to start a campfire by focusing sunlight with the lens from a nearsighted friend’s glasses. Predict whether this will work, and explain your prediction.