A convex (converging) lens can form a virtual, upright, magnified image when the object is placed inside its focal length.
The image appears on the same side of the lens as the object and is therefore virtual.
For a comfortable viewing distance the image is usually formed at the eye’s near point (≈25 cm).
Thin Lens Equation
The relationship between object distance \(u\), image distance \(v\) and focal length \(f\) is given by
\$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\$
All distances are measured from the lens centre. In the sign convention used here:
Object distance \(u\) is positive if the object is on the left side of the lens.
Image distance \(v\) is positive if the image is on the right side (real image) and negative if on the left side (virtual image).
Focal length \(f\) is positive for a converging lens.
Magnification
The linear magnification \(m\) is
\$m=-\frac{v}{u}=\frac{h'}{h}\$
where \(h\) and \(h'\) are the heights of the object and image respectively. A negative sign indicates that a real image is inverted; for a virtual image \(v\) is negative, so \(m\) is positive and the image is upright.
Using a Lens as a Magnifying Glass
Select a convex lens with a suitable focal length (typically 5–10 cm).
Place the object a short distance from the lens, inside its focal length (\(u < f\)).
Adjust the distance until the virtual image is at the near point (≈25 cm) for the viewer.
Hold the lens so that the image appears clear and the eye can comfortably focus on it.
Conditions for a Useful Magnifying Glass
The object must be within the focal length of the lens.
The virtual image should be at or beyond the near point to avoid eye strain.
Lens quality (absence of aberrations) improves clarity and magnification.
Example Calculations
Object Distance \(u\) (cm)
Image Distance \(v\) (cm)
Magnification \(m\)
5
-10
2.0
7
-23.33
3.33
9
-45
5.0
Practical Tips
Use a hand‑held lens with a small diameter to reduce spherical aberration.
Hold the lens close to the eye to minimise the eye’s accommodation effort.
For larger magnification, use a lens with a shorter focal length, but be aware of increased distortion.
Suggested diagram: A single convex lens with an object placed within the focal length, showing a virtual, upright, magnified image on the same side of the lens as the object.