Concave Mirrors
Ray diagrams and the five object positions
Do Now: A makeup or shaving mirror makes your face look bigger. What kind of mirror is it, and where must your face be?
A concave mirror, with your face closer to the mirror than its focal point. By the end of this lesson you will be able to prove it with a ray diagram.
A. The Three Principal Rays
Light leaves the top of the object in every direction. Three rays are easy to predict, and any two of them locate the image.
Ray 1 — Parallel Ray
Travels parallel to the principal axis, then reflects through F.
Ray 2 — Focal Ray
Travels through F, then reflects parallel to the principal axis.
Ray 3 — Center Ray
Travels through C, hits the mirror straight on, and reflects back on itself.
The top of the image is where the reflected rays cross. If they spread apart, trace them backward (dashed lines) behind the mirror — that makes a virtual image.
B. Five Object Positions
Start with the object far away and move it toward the mirror.
Case 1: Object beyond C
Click Next to draw the ray diagram step by step.
Describe the image using L-O-S-T.
L: Between C and F O: Inverted S: Smaller T: Real
Case 2: Object at C
Click Next to draw the ray diagram step by step.
Describe the image using L-O-S-T.
L: At C O: Inverted S: Same size T: Real
Case 3: Object between C and F
Click Next to draw the ray diagram step by step.
Describe the image using L-O-S-T.
L: Beyond C 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 reflected rays come out parallel and never meet, so no image forms.
Case 5: Object between F and the mirror
Click Next to draw the ray diagram step by step.
Describe the image using L-O-S-T.
L: Behind the mirror O: Upright S: Larger T: Virtual
Summary: Concave Mirror
| Object Location | Image Location | Orientation | Size | Type |
|---|---|---|---|---|
| Beyond C | Between C and F | Inverted | Smaller | Real |
| At C | At C | Inverted | Same size | Real |
| Between C and F | Beyond C | Inverted | Larger | Real |
| At F | No image forms | — | — | — |
| Between F and the mirror | Behind the mirror | Upright | Larger | Virtual |
As the object moves toward F, the real image moves away from the mirror and gets larger. Once the object is inside F, the image flips to virtual and upright.
Explore: Concave Mirror
Drag the orange object. Turn rays on and off with the check boxes.
C. Concave Mirrors at Work
Flashlights & headlights: the bulb sits at F, so the reflected light leaves as a parallel beam (Case 4 in reverse).
Makeup & shaving mirrors: your face is inside F, so you see a larger, upright, virtual image (Case 5).
Reflecting telescopes: a large concave mirror gathers light from distant stars and focuses it near F.
Solar cookers: sunlight arrives as parallel rays and is concentrated at F.
Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. A ray travels parallel to the principal axis and strikes a concave mirror. After reflecting, it passes through
2. An object is placed beyond C in front of a concave mirror. The image is
3. Where should an object be placed so a concave mirror makes a real image the same size as the object?
4. A car headlight bulb is placed at the focal point of a concave mirror. The reflected light
5. Which object position gives a virtual image in a concave mirror?
Makeup Mirrors and Headlights
A concave mirror has a focal length of 20. cm. Engineers use concave mirrors in makeup mirrors, car headlights, and solar cookers, placing the object or light source at different distances from the mirror.
A person’s face is 10. cm from the mirror (inside the focal point). Which describes the image?
▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)
Challenge score: 0 / 6
C1. Place a check mark in three boxes to indicate the object distances at which this mirror (f = 20. cm) forms a real image.
C2. In a headlight, the bulb is placed exactly at the focal point. What happens to the reflected light?
C3. An object is placed 60. cm in front of this mirror. Substitute numerical values into a mathematical representation that can be used to determine the image distance. Then calculate the image distance.
C4. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
C5. An object is placed beyond the center of curvature (beyond 40. cm). Which describes the image?
C6. An engineer is designing a solar cooker using a concave mirror. Identify one benefit and one drawback of using a mirror with a larger diameter (same focal length).