Ray diagram of a concave mirror when the object is between F and P
The image is behind the mirror: virtual and erect, enlarged.
The ray diagram
Drag the object or type values. Signs follow the New Cartesian convention: distances are measured from the pole or optical centre, along the incident light is positive, against it negative, and heights above the axis are positive. So u is negative for a real object.
Concave mirror of focal length -10 cm. An object +2 cm tall at u = -5 cm: the image is at v = +10 cm, virtual, erect, enlarged.
Show the working
- f = R/2 = -20/2 = -10 cm, u = -5 cm (the object is in front, so u is negative), h = +2 cm.
- 1/v = 1/f - 1/u = 1/(-10) - 1/(-5) = 5/50 = 1/10
- v = +10 cm: positive, so the image is behind the mirror and virtual.
- m = -v/u = -(+10)/(-5) = +2: positive, so erect, and enlarged.
- h′ = m × h = +2 × +2 = +4 cm
Take f = 10 cm and the object at 5 cm
- f = R/2 = -20/2 = -10 cm, u = -5 cm (the object is in front, so u is negative), h = +2 cm.
- 1/v = 1/f - 1/u = 1/(-10) - 1/(-5) = 5/50 = 1/10
- v = +10 cm: positive, so the image is behind the mirror and virtual.
- m = -v/u = -(+10)/(-5) = +2: positive, so erect, and enlarged.
- h′ = m × h = +2 × +2 = +4 cm
Image formation by a concave mirror
| Object | Image | Size | Nature |
|---|---|---|---|
| At infinity | At the focus F | Highly diminished, point-sized | Real and inverted |
| Beyond C | Between F and C | Diminished | Real and inverted |
| At C | At C | Same size | Real and inverted |
| Between C and F | Beyond C | Enlarged | Real and inverted |
| At F | At infinity | Highly enlarged | Real and inverted |
| Between P and F | Behind the mirror | Enlarged | Virtual and erect |
The rays to use
- A ray parallel to the principal axis passes through the focus F after reflection.
- A ray through the centre of curvature C hits the mirror head on and reflects back along the same path.
- A ray through the focus F reflects parallel to the principal axis.
- A ray striking the pole P obliquely reflects at the same angle on the other side of the axis.
In real life
- Shaving and make-up mirrors, and dentists' mirrors: an enlarged, erect image of a face or a tooth.
Quick answers
Where is the image when the object is between F and P of a concave mirror?
The image is behind the mirror: virtual and erect, enlarged. With f = 10 cm and the object at 5 cm, v = +10 cm and m = +2.
Is this image real or virtual?
Virtual: the rays only appear to meet when traced back, so no screen can catch it. Virtual images formed by one mirror or lens are erect.
Where is this used?
Shaving and make-up mirrors, and dentists' mirrors: an enlarged, erect image of a face or a tooth.