JEE Advanced · 2006 · 09 Apr 2006 · Geometrical Optics

Graph of position of image vs position of point object from a convex lens is shown. Then, focal length of the lens is

(A)0.50 ± 0.05 cm
(B) $0.50 \pm 0.10 cm$
(C) $5.00 \pm 0.05 cm$
(D) $5.00 \pm 0.10 cm$ ✓ Correct

Answer: (D)

Solution

From the lens formula:

\frac{1}{f} = \frac{1}{v} - \frac{1}{u}

From the graph, we can read values of u and v. Using these values, we get

f = 5

cm.

For error analysis, using

f = \frac{uv}{u + v}

\frac{Δ f}{f} = \frac{Δ u}{u} + \frac{Δ v}{v} + \frac{∣Δ u ∣ + ∣Δ v ∣}{∣ u ∣ + ∣ v ∣}

From the graph's least count and reading errors,

Δ f \approx 0.15

cm for

f = 5

cm.

The most appropriate answer considering significant figures and error propagation is

5.00 \pm 0.10

cm, which is option (D).

JEE Advanced · 2006 · 09 Apr 2006 · Single correct option

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