In an experiment with a convex lens, The plot of the image distance (v′) against the object distance (μ′) measured from the focus gives a curve v′ μ′=225. If all the distances are measured in cm. The magnitude of the focal length of the lens is ___________ cm.

Solution

Physics sir · 3 steps

Distances measured from the foci multiply to f². That is Newton's lens formula, so take the square root.

1. Shift the origin. For a real image, the object sits a distance u' beyond the first focus and the image sits v' beyond the second focus. So the usual distances from the lens are |u| = f + u' and v = f + v'.
2. Use the lens formula. Put these into 1/v - 1/u = 1/f, which gives 1/(f + v') + 1/(f + u') = 1/f. Cross-multiplying gives 2f² + f(u' + v') = f² + f(u' + v') + u'v', and the f(u' + v') terms cancel.

   u'v' = f²

3. So. f² = 225 cm², so f = √225 = 15 cm. The answer is 15.

The common slip: 225. Reading the constant 225 as the focal length gives 225. The product u'v' equals f², so you still need the square root.

The idea to keep. When distances are measured from the foci, not from the lens, use Newton's form x₁ x₂ = f². A rectangular hyperbola xy = c on such a plot means f = √c.

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