Light – Reflection and Refraction · Lesson 3 of 15
Image Formation by Spherical Mirrors
“Move the candle a little and the image starts changing seats.”
• Distinguish real and virtual images formed by mirrors. • Relate image position, size and orientation to object position. • Describe the six object positions used for a concave mirror. • Interpret the complete concave-mirror image table. • Explain why only some mirror images can be caught on a screen.
Move a candle toward a concave mirror and the image on a screen does not stay fixed. It shifts, changes size and may eventually disappear from the screen even though an image is still visible in the mirror. The object position relative to P, F and C controls all these changes.
Real and Virtual Images
An image formed where reflected rays actually meet. It can be received on a screen and is inverted for the situations considered here.
An image formed where the backward extensions of reflected rays appear to meet. It cannot be obtained on a screen and is erect for the situations considered here.
A screen records light only when rays physically arrive and converge on it. This is why a real image can be projected, while a virtual image cannot. Seeing a virtual image is still possible because the eye receives diverging rays and traces them backward.
Experimental Study
First estimate the focal length of a concave mirror using a distant object. Mark P, F and C on a long table so that PF = f and PC = 2f. Place a bright object successively at different positions and move a screen until a sharp image forms. For each position, record image position, relative size, orientation and whether it is obtained on the screen.
| Object position | Image position | Relative size | Nature |
|---|---|---|---|
| At infinity | At 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 | No finite screen position | Rays emerge parallel |
| Between P and F | Behind the mirror | Enlarged | Virtual and erect |
Reading the Pattern
When a distant object approaches C from beyond, its real image moves away from F toward C and grows. At C, object and image are equally far from the mirror and equal in size. As the object moves from C toward F, the image travels beyond C and becomes enlarged. At F, reflected rays are parallel, so no finite screen can collect them. Inside F, the rays diverge after reflection and their backward extensions form an enlarged virtual image behind the mirror.
Problem
A candle placed in front of a concave mirror forms an enlarged image that can be obtained on a screen beyond C. Where is the candle?
- 1.A screen image must be real, so the object is outside the focal point.
- 2.An enlarged real image beyond C is the characteristic result for an object between C and F.
- 3.Therefore the candle lies between C and F.
- 4.The image is real, inverted and enlarged.
Activity
Purpose: Build the image table from observation. Use a concave mirror on a stand, a small candle and a white screen. Keep the flame well away from other materials. Place the object at each listed position and move the screen until the image is sharp. For the position between P and F, remove the screen and look into the mirror. The failure to obtain this last image on a screen is evidence that it is virtual.
At F, saying that no image exists is misleading. The reflected rays are parallel and the image is described as being at infinity; it simply cannot be collected at any finite screen position.
Quiz
Which image can be obtained on a screen?
Where is the image when an object is at C of a concave mirror?
An object between P and F produces which image?
Why is no sharp image found on a finite screen when the object is at F?
An image between F and C is diminished and real. Where is the object?
Practice Problems
- State the image formed when an object is at C. Solution: The image is at C, real, inverted and the same size as the object.
- An image is virtual, erect and enlarged. Identify the mirror and object region. Solution: A concave mirror produces this result when the object is between P and F.
- A distant tree is viewed using a concave mirror. Describe its image. Solution: It forms near F as a highly diminished, real and inverted image.
- Why does a virtual image remain visible although a screen cannot capture it? Solution: Diverging reflected rays enter the eye, which traces them backward to an apparent source. They do not physically converge at that source, so a screen there receives no focused light.
- Arrange the real-image positions as an object moves from infinity toward F. Solution: The image moves from F toward C, reaches C when the object is at C, then moves beyond C and finally toward infinity as the object approaches F.
Key Takeaways
• Real images form by actual convergence and can be caught on a screen. • Virtual images form by apparent convergence of backward extensions. • A concave mirror forms real inverted images when the object is outside F. • At C, the image is at C and has the same size as the object. • At F, reflected rays are parallel and the image is at infinity. • Between P and F, the image is virtual, erect and enlarged.