In an experiment to measure the focal length (f) of a convex lens, the magnitude of object distance (x) and the image distance (y) are measured with reference to the focal point of the lens. The y-x plot is shown in figure.
The focal length of the lens is ________ cm.

Solution

Physics sir · 4 steps

Distances measured from the focus mean Newton's formula xy = f²; read one clean point off the curve.

1. Newton's lens formula. When object and image distances are measured from the two focal points, the lens formula becomes xy = f². So the curve in the plot is a hyperbola, and the product xy is the same at every point on it.

   x y = f²

2. Pick point C. Point C sits exactly on the dashed grid lines at x = 20 cm and y = 20 cm. It is also where the straight line x + y = 40 just touches the curve. That is the symmetric point x = y = f.
3. Put in numbers. f² = 20 × 20 = 400 cm², so f = 20 cm. Points D and E agree: roughly 30.5 × 13.1 and 41 × 9.7 both come to about 400.
4. So. The focal length of the lens is 20 cm.

The common slip: 10. Using 1/f = 1/v - 1/u with 20 cm and 20 cm treats these as distances from the lens and gives 10. Here they are measured from the focal points.

The idea to keep. If distances are measured from the focal points, use xy = f². The point on the curve where x = y gives f directly.

Answer from the NTA final answer key. Solution by PrepWiser.