A concave lens produces a virtual image. The focal length of the lens is 3 cm and the object is at a position 9 cm away from the lens. Find the magnification.

Question

BlackTom AI · Accepted Answer

Using the thin-lens equation with sign convention (object and virtual image to the left are negative), take f = -3 cm (concave lens) and u = -9 cm (real object to the left).

1) Relevant knowledge points and concepts
- Thin-lens equation: 1/f = 1/v + 1/u (with sign convention).
- Image distance v negative for a virtual image on the same side as the object.
- Lateral magnification: m = v/u (sign included); a positive m means upright image, magnitude |m| gives size ratio.

2) Step-by-step reasoning
Apply the lens equation to find v, then compute m = v/u.

3) Calculations with intermediate steps
1/f = 1/v + 1/u
Substitute f = -3 cm, u = -9 cm:
1/(-3) = 1/v + 1/(-9)
-1/3 = 1/v - 1/9
Solve for 1/v:
1/v = -1/3 + 1/9 = (-3 + 1)/9 = -2/9
Therefore v = -9/2 = -4.5 cm (negative sign indicates a virtual image 4.5 cm on the object side of the lens).

Magnification:
m = v/u = (-4.5)/(-9) = 0.5

4) Why the correct answer is correct
The concave lens (f < 0) with the object at 9 cm produces a virtual image at -4.5 cm, and the ratio v/u gives m = 0.5. The positive sign indicates the image is upright and its size is half that of the object, which matches the physical behavior of a concave (diverging) lens producing a reduced, upright virtual image when the object is placed outside the focal length.

5) Why the other choices are incorrect
a. 1 — would mean the image is same size as the object; calculation shows m = 0.5, not 1.
c. 0.33 — could come from an incorrect arithmetic or wrong sign convention (e.g., miscomputing v = -3), but it does not follow from correct application of the lens formula.
d. 3 — would imply a magnified image three times larger; concave lenses do not produce a magnified virtual image for an object placed outside the focal length, and the correct calculation yields 0.5.

6) Conclusion
The magnification is 0.5. This confirms the provided correct answer: b. 0.5.

A concave lens produces a virtual image. The focal length of the lens is 3 cm and the object is at a position 9 cm away from the lens. Find the magnification.单项选择题

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