The focal length of a convex lens can be determined experimentally using the object-image distance method or mathematically using the lens equation. The most practical approach is the object-image distance method: place the lens between a light source and a screen, adjusting the lens position until a sharp, inverted image forms on the screen. Measure the distance from the object to the lens (u) and from the lens to the image (v), then apply the thin lens equation: 1/f = 1/u + 1/v, solving for f (focal length). Alternatively, use the displacement method: if the object and screen are fixed at distance D apart, move the lens until you find two positions that produce sharp images. Measure the distance d between these two positions; the focal length is calculated as f = (D² − d²)/(4D). Another quick method is the Bessel method, which relies on the same principle but offers improved precision. For a rough estimate without equipment, focus sunlight onto paper using the lens—the distance from the lens to the focused point is approximately the focal length. Convex lenses converge light to a real focal point, so any method involving focusing light (sunlight or an illuminated object) will reveal this distance. These experimental approaches work because they exploit the fundamental property of convex lenses: they bend parallel rays to converge at a single focal point.