Ray diagram of a concave mirror: all 6 cases
A concave mirror forms a real, inverted image for every object position except between F and P, where the image is virtual, erect and 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 = -15 cm: the image is at v = -30 cm, real, inverted, enlarged.
Show the working
- f = R/2 = -20/2 = -10 cm, u = -15 cm (the object is in front, so u is negative), h = +2 cm.
- 1/v = 1/f - 1/u = 1/(-10) - 1/(-15) = -5/150 = -1/30
- v = -30 cm: negative, so the image is in front of the mirror and real.
- m = -v/u = -(-30)/(-15) = -2: negative, so inverted, and enlarged.
- h′ = m × h = -2 × +2 = -4 cm
6 positions of the object
- Object at infinity At the focus F. Real and inverted, highly diminished, point-sized.
- Object beyond C Between F and C. Real and inverted, diminished.
- Object at C At C. Real and inverted, same size.
- Object between C and F Beyond C. Real and inverted, enlarged.
- Object at F At infinity. Real and inverted, highly enlarged.
- Object between P and F Behind the mirror. Virtual and erect, enlarged.
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.
Object between C and F, f = 10 cm
- f = R/2 = -20/2 = -10 cm, u = -15 cm (the object is in front, so u is negative), h = +2 cm.
- 1/v = 1/f - 1/u = 1/(-10) - 1/(-15) = -5/150 = -1/30
- v = -30 cm: negative, so the image is in front of the mirror and real.
- m = -v/u = -(-30)/(-15) = -2: negative, so inverted, and enlarged.
- h′ = m × h = -2 × +2 = -4 cm
Quick answers
How many cases of image formation are there for a concave mirror?
Six: the object at infinity, beyond C, at C, between C and F, at F, and between F and P.
When does a concave mirror form a virtual image?
Only when the object is between the focus F and the pole P. The image is then behind the mirror, erect and enlarged.
When is the image the same size as the object?
When the object is at the centre of curvature C. The image also forms at C, real and inverted.