How can a lens make both real and virtual images?
How can a lens make both real and virtual images?
- Place the object at three focal lengths.
- Move toward the focal plane and watch the image distance.
- Move inside the focus and inspect backward extensions.
What to measure
f, dₒ and dᵢ in m; negative dᵢ denotes a virtual image.
The idea underneath
A converging thin lens redirects paraxial rays so parallel light reaches the focal point. An object outside the focal length makes a real inverted image on the other side. Inside the focal length, outgoing rays diverge and their backward extensions locate an upright virtual image. At exactly one focal length the image is at infinity; the readout handles this singular case explicitly. The glass shape is illustrative; the calculation uses the thin-lens equation.
1/f=1/dₒ+1/dᵢ · M=−dᵢ/dₒf, dₒ and dᵢ in m; negative dᵢ denotes a virtual image.
Build the argument
- Identify the optical axis and the normal to each interface.
- Apply reflection, Snell’s law, or the paraxial lens equation according to the model.
- Check limiting cases: equal indices, object at the focal plane, or a slit much wider than the wavelength.
Worked example 1
f=1 m and dₒ=3 m give dᵢ=1.5 m and M=−0.5.
Worked example 2
f=1 m and dₒ=0.5 m give dᵢ=−1 m and M=2.
Applications
Cameras, microscopes and fibre links combine geometric paths with wave limitations. An image can be sharp geometrically and still be limited by diffraction.
Common misconception
Angles are measured from the normal, not the surface. A virtual image is located by backward ray extensions; no rays physically converge there.
A further investigation
Locate the object that makes a real image of equal size.
Check your understanding
A negative image distance means…
- Virtual image
- No light
- Negative energy
Explanation
Backward extensions locate a virtual image. Equal real size occurs at dₒ=2f.
Model limits
Paraxial thin converging lens. No aberrations, thickness, dispersion or diffraction.