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Physics
Thấu kính phân kì và gương cầu
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Move an object, change focal length and compare the position and size of images formed by a diverging lens, convex mirror and concave mirror.
Virtual image · upright · smaller
Drag the object closer or farther
Incident ray / Refracted rayBackward extension (virtual image)
Distance is measured from the object to the optical centre or mirror vertex O.
Position presets
Virtual image
Upright · Smaller
The outgoing rays diverge. Their backward extensions meet between the lens and its focus, producing an upright, smaller virtual image.
- Image distance |d′|
- 15 cm · In front of the lens, on the object side
- Magnification m
- 0.25 ×
- Image height |h′|
- 3 cm
Optical relationships
1/f = 1/d + 1/d′
m = −d′/d = h′/h
With numbers
1/(−20) = 1/60 + 1/(−15)
m = −(−15)/60 = 0.25
d > 0. f is negative for a diverging lens and convex mirror, and positive for a concave mirror. d′ > 0: real image; d′ < 0: virtual image. m < 0: inverted image.
Model notes
- This model uses a thin lens and paraxial spherical mirrors, with a real object to the left of the instrument. Distances and heights are measured in cm.
- Rays refract or reflect in the plane through the optical centre or mirror vertex. Curved shapes identify the instrument; the model does not accurately trace rays far from the axis.
- For readability the vertical axis is drawn magnified relative to the horizontal axis (about 2–4 times depending on the frame; the factor is shown in the corner). This changes only the drawing, not the image position, its calculated size or where the rays meet.
- Aberration, diffraction, brightness, aperture and a projection screen are not modelled. Dashed extensions are not paths travelled by light.
- Focal length is negative for a diverging lens and convex mirror, and positive for a concave mirror. Image distance d′ is positive for real images and negative for virtual images; negative magnification means an inverted image.
- An object at the focus of a concave mirror produces parallel reflected rays with no image at a finite distance. Off-screen images retain their calculated positions and are never placed at the edge of the view.