Light – Reflection and Refraction · Lesson 5 of 15
Image Formation by Concave Mirror
“This mirror can shrink a tree, enlarge a tooth, and still look innocent.”
• Construct ray diagrams for all six concave-mirror object positions. • Predict image position, size, orientation and nature. • Connect object motion with image motion. • Choose concave mirrors for suitable practical uses. • Explain each use through convergence or magnification.
The same concave mirror can make a tiny image of a distant tree, an equal-sized image of a nearby candle, or a magnified face in a shaving mirror. The mirror has not changed; the position of the object relative to F and C has.
Six Image-Formation Cases
| Object | Construction result | Image |
|---|---|---|
| At infinity | Parallel rays meet at F | At F; point-sized; real and inverted |
| Beyond C | Reflected rays meet between F and C | Diminished; real and inverted |
| At C | Reflected rays return to C | Same size; real and inverted |
| Between C and F | Reflected rays meet beyond C | Enlarged; real and inverted |
| At F | Reflected rays are parallel | At infinity; no finite screen image |
| Between F and P | Backward extensions meet behind mirror | Enlarged; virtual and erect |
Understanding the Transitions
For an object outside F, the image is real and inverted. As the object moves from infinity toward F, the image moves from F toward infinity and generally grows. Crossing F changes the geometry: reflected rays cease to converge in front of the mirror, so the image becomes virtual, erect and located behind the mirror.
Problem
A distant building is beyond C. Predict its image and explain the construction.
- 1.Draw a ray parallel to the axis; it reflects through F.
- 2.Draw a ray through C; it retraces its path.
- 3.The rays meet between F and C.
- 4.The image is real, inverted and diminished, so a screen can receive it.
Problem
Where should an object be placed to obtain a real image of the same size?
- 1.Same size is the special case in which object and image are symmetrically located at C.
- 2.Place the object at C, equal to two focal lengths from P.
- 3.The image forms at C, is real and inverted, and has magnification -1.
Problem
A dentist needs an upright enlarged view of a tooth. Where must the tooth be relative to the mirror?
- 1.An upright enlarged image from a concave mirror must be virtual.
- 2.That case occurs only when the object lies between P and F.
- 3.The tooth must therefore be closer to the mirror than its focal point.
- 4.The image appears behind the mirror and cannot be projected on a screen.
Detailed Ray Diagrams for the Six Cases
The table above gives the final result of each case. The following constructions show how those results arise. In every diagram, blue lines are incident rays, red lines are reflected rays, the orange arrow is the object and the purple arrow or point indicates the image. Solid lines represent actual light paths. Dashed purple lines are used only when backward extensions are needed to locate a virtual image.
Object at Infinity
An object at a very large distance sends rays that reach the concave mirror almost parallel to the principal axis. After reflection, these parallel rays converge at the principal focus. Because the reflected rays actually meet, the image is real. The rays from different points of a distant object form a very small inverted image close to the principal focus. In the ideal limiting case shown here, the image is represented by a point at the principal focus.
• Object position: At infinity. • Image position: At the principal focus. • Relative size: Highly diminished or point-sized. • Orientation: Inverted. • Nature: Real. • Screen test: The image can be received on a screen placed at the principal focus.
Object Beyond the Centre of Curvature
Place the object farther from the mirror than the centre of curvature. From the top of the object, draw one ray parallel to the principal axis; it reflects through the principal focus. Draw a second ray through the centre of curvature; it strikes the mirror normally and retraces its path. The two reflected rays intersect between the centre of curvature and principal focus. Their actual intersection produces a real image. The image arrow is below the principal axis, showing that it is inverted, and it is shorter than the object arrow, showing that it is diminished.
• Object position: Beyond the centre of curvature. • Image position: Between the centre of curvature and principal focus. • Relative size: Diminished. • Orientation: Inverted. • Nature: Real. • Screen test: The image can be received on a screen.
Object at the Centre of Curvature
Place the object at the centre of curvature. A ray parallel to the principal axis reflects through the principal focus. A second ray directed through the principal focus reflects parallel to the principal axis. These reflected rays meet at the centre of curvature. The image forms at the same distance from the mirror as the object. Its arrow has the same height as the object but points below the principal axis, so the image is real, inverted and the same size. The magnification is −1.
• Object position: At the centre of curvature. • Image position: At the centre of curvature. • Relative size: Same size as the object. • Orientation: Inverted. • Nature: Real. • Magnification: −1. • Screen test: The image can be received on a screen.
Object Between the Centre of Curvature and Principal Focus
Place the object between the centre of curvature and principal focus. Draw a ray parallel to the principal axis; after reflection it passes through the principal focus. Draw another ray through the principal focus; after reflection it travels parallel to the principal axis. The reflected rays meet beyond the centre of curvature. Their intersection is below the principal axis and farther from the mirror than the object, producing a real, inverted and enlarged image. As the object moves closer to the principal focus, this image moves farther away and becomes larger.
• Object position: Between the centre of curvature and principal focus. • Image position: Beyond the centre of curvature. • Relative size: Enlarged. • Orientation: Inverted. • Nature: Real. • Screen test: The image can be received on a screen.
Object at the Principal Focus
Place the base of the object at the principal focus. A ray from the object tip that is parallel to the principal axis reflects through the principal focus. A second ray directed through the centre of curvature retraces its path. In this limiting position, the two reflected rays from the object tip emerge parallel to each other and therefore do not meet at any finite distance. The image is described as forming at infinity. It is real and inverted in the limiting theoretical sense and is highly enlarged, but no finite screen position can capture the complete image.
• Object position: At the principal focus. • Image position: At infinity. • Relative size: Highly enlarged. • Orientation: Inverted. • Nature: Real in the limiting theoretical sense. • Screen test: No finite screen position captures the complete image.
Object Between the Principal Focus and Pole
Place the object between the principal focus and pole. A ray parallel to the principal axis reflects through the principal focus. A second ray strikes the pole and reflects according to the law of reflection. The reflected rays spread apart in front of the mirror, so they cannot form a real image there. Extend both reflected rays backward behind the mirror using dashed lines. Their extensions meet behind the mirror, locating a virtual image. The image arrow is upright and taller than the object arrow, so the image is erect and enlarged. Because no real rays pass through the image position, it cannot be projected onto a screen.
• Object position: Between the principal focus and pole. • Image position: Behind the mirror. • Relative size: Enlarged. • Orientation: Erect. • Nature: Virtual. • Screen test: The image cannot be received on a screen.
Uses of Concave Mirrors
| Use | Required property |
|---|---|
| Torch, searchlight and headlight reflector | A source near F produces a strong nearly parallel beam |
| Shaving mirror | A face between P and F gives an enlarged erect image |
| Dentist's mirror | A nearby tooth gives an enlarged erect image |
| Solar furnace | Parallel sunlight is concentrated near F to produce heat |
Activity
Draw one diagram for each object position using any two standard rays. Under every diagram, state image position, relative size, orientation and nature. Compare the six drawings as a sequence rather than memorising isolated cases. The movement of the ray intersection makes the pattern easier to retain.
Quiz
Which object position gives a same-sized image?
When is a concave-mirror image virtual and erect?
Why is a concave mirror used in a solar furnace?
A real enlarged image forms beyond C. Where is the object?
A bulb placed near F in a headlight produces what kind of beam?
Practice Problems
- Predict the image of an object beyond C. Solution: It forms between F and C, diminished, real and inverted.
- Where should an object be placed for magnification -1? Solution: At C; the real inverted image also forms at C and is the same size.
- Why cannot a concave shaving mirror be held too far from the face? Solution: Beyond F the image becomes real and inverted. For an erect enlarged view, the face must remain between P and F.
- Explain the role of a concave mirror in a torch. Solution: With the light source close to F, reflected rays emerge approximately parallel, producing a strong directed beam.
- An object moves from C toward F. Describe the image change. Solution: The real inverted image moves from C to beyond C and increases in size, approaching infinity as the object approaches F.
Key Takeaways
• A concave mirror can form real or virtual images depending on object position. • All finite objects outside F form real inverted images. • At C, image and object have equal size and occupy C on opposite orientations. • Inside F, the image is virtual, erect and enlarged. • Concave mirrors provide parallel beams when a source is near F. • They also provide magnification or concentrate sunlight in practical devices.