Converging Lenses
Cameras, projectors, and magnifying glasses
Do Now: A magnifying glass can make a bug look huge, or focus sunlight into a tiny bright dot. How can one lens do both?
It depends on where the object is compared to the focal point. Sunlight arrives as parallel rays and meets at F. A bug inside F gives a larger, upright, virtual image.
A. The Three Principal Rays
A lens has a focal point on each side. Light enters from the left and leaves on the right.
Ray 1 — Parallel Ray
Travels parallel to the principal axis, then refracts through F on the far side.
Ray 2 — Focal Ray
Travels through F on the near side, then leaves the lens parallel.
Ray 3 — Center Ray
Goes through the center of the lens without bending.
B. Five Object Positions
The pattern matches the concave mirror, with 2F in place of C — but real images form on the other side of the lens.
Case 1: Object beyond 2F
Click Next to draw the ray diagram step by step.
Describe the image using L-O-S-T.
L: Between F and 2F (other side) O: Inverted S: Smaller T: Real
Case 2: Object at 2F
Click Next to draw the ray diagram step by step.
Describe the image using L-O-S-T.
L: At 2F (other side) O: Inverted S: Same size T: Real
Case 3: Object between 2F and F
Click Next to draw the ray diagram step by step.
Describe the image using L-O-S-T.
L: Beyond 2F (other side) O: Inverted S: Larger T: Real
Case 4: Object at F
Click Next to draw the ray diagram step by step.
Describe the image using L-O-S-T.
The refracted rays come out parallel and never meet, so no image forms.
Case 5: Object between F and the lens
Click Next to draw the ray diagram step by step.
Describe the image using L-O-S-T.
L: Same side as the object O: Upright S: Larger T: Virtual
Summary: Converging Lens
| Object Location | Image Location | Orientation | Size | Type |
|---|---|---|---|---|
| Beyond 2F | Between F and 2F (other side) | Inverted | Smaller | Real |
| At 2F | At 2F (other side) | Inverted | Same size | Real |
| Between 2F and F | Beyond 2F (other side) | Inverted | Larger | Real |
| At F | No image forms | — | — | — |
| Between F and the lens | Same side as the object | Upright | Larger | Virtual |
Explore: Converging Lens
Drag the orange object. Turn rays on and off with the check boxes.
C. Converging Lenses at Work
Camera & your eye (Case 1): a faraway scene makes a small, inverted, real image on the sensor or retina.
Photocopier (Case 2): a same-size copy.
Projector (Case 3): a small slide or chip just outside F makes a large image on the screen. That’s why projector slides go in upside down!
Magnifying glass (Case 5): the object is inside F, giving a larger, upright, virtual image.
Glasses for farsightedness: converging lenses help the eye focus on nearby objects.
Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. A ray passes through the near-side focal point of a converging lens. After the lens it
2. A camera photographs a building far away. The image on the sensor is
3. To use a converging lens as a magnifying glass, the object must be
4. A movie projector makes a huge image on a screen. Where is the film compared to the lens?
5. A ray of light passes through the exact center of a thin lens. It
Designing a Classroom Projector
A projector uses a converging lens with a focal length of 10. cm to project a small, brightly lit image onto a large screen across the room.
Where must the small object (the image source) be placed to produce a large real image on the screen?
▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)
Challenge score: 0 / 6
C1. A magnifying glass is a converging lens. Where is the object placed?
C2. The slide is placed 12. cm from the lens. Substitute numerical values into a mathematical representation that can be used to determine where the screen must be placed. Then calculate the image distance.
C3. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response.
C4. The slide’s picture is 2.0 cm tall and is 12. cm from the lens, producing an image 60. cm from the lens. Determine the height of the image on the screen.
C5. The projector’s object is moved closer to F (but still beyond it). How does the image change?
C6. The projector company considers using a lens with a larger diameter but the same focal length. Identify one benefit and one drawback of this design change.