Figure shows a convex lens cut symmetrically into two equal halves and separated laterally by a distance h. A point object O placed symmetrically at a distance 30 cm, from the lens halves, forms two images separated by a distance d. A plot of d versus h is shown in figure. The focal length of the lens is :-

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TestHub · Accepted Answer

Each half-lens has its optical axis displaced by h/2; image shifts by |m|h/2 from it.

Total separation $d = 2∣ m ∣ \frac{h}{2} + h$ .

From the graph, h = 1 cm gives d = 3 cm ⇒ |m| = 2.

$m = \frac{v}{u} = \frac{f}{u + f}, u = - 30 cm$

Erected image: m = +2 ⇒ $\frac{f}{f - 30} = 2 \Rightarrow f = 30 \dots f = 40 cm$ ⇒ (B) CORRECT

Inverted image: m = -2 ⇒ $\frac{f}{f - 30} = - 2 \Rightarrow f = 20 cm$ ⇒ (D) CORRECT

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