Ray diagram of a concave mirror when the object is at C
The image is at C: real and inverted, same size.
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 = -20 cm: the image is at v = -20 cm, real, inverted, same size.
Show the working
- f = R/2 = -20/2 = -10 cm, u = -20 cm (the object is in front, so u is negative), h = +2 cm.
- 1/v = 1/f - 1/u = 1/(-10) - 1/(-20) = -10/200 = -1/20
- v = -20 cm: negative, so the image is in front of the mirror and real.
- m = -v/u = -(-20)/(-20) = -1: negative, so inverted, and the same size.
- h′ = m × h = -1 × +2 = -2 cm
Take f = 10 cm and the object at 20 cm
- f = R/2 = -20/2 = -10 cm, u = -20 cm (the object is in front, so u is negative), h = +2 cm.
- 1/v = 1/f - 1/u = 1/(-10) - 1/(-20) = -10/200 = -1/20
- v = -20 cm: negative, so the image is in front of the mirror and real.
- m = -v/u = -(-20)/(-20) = -1: negative, so inverted, and the same size.
- h′ = m × h = -1 × +2 = -2 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
- Finding the focal length in the lab: when the image is the same size as the object, both are at C and u = v = 2f.
Quick answers
Where is the image when the object is at C of a concave mirror?
The image is at C: real and inverted, same size. With f = 10 cm and the object at 20 cm, v = -20 cm and m = -1.
Is this image real or virtual?
Real: the rays actually meet there, so the image can be caught on a screen. Real images formed by one mirror or lens are inverted.
Where is this used?
Finding the focal length in the lab: when the image is the same size as the object, both are at C and u = v = 2f.