An optical bench has $$1.5$$ m long scale having four equal divisions in each cm. While measuring the focal length of a convex lens, the lens is kept at $$75$$ cm mark of the scale and the object pin is kept at $$45$$ cm mark. The image of the object pin on the other side of the lens overlaps with image pin that is kept at $$135$$ cm mark. In this experiment, the percentage error in the measurement of the focal length of the lens is $$_____$$

Question

Infinity Learn · Accepted Answer

$$1v$$−$$1u=1f$$⇒$$160+130=1f$$⇒$$f=20cmu=x2$$−$$x1$$⇒Δ$$u=$$Δ$$x2+$$Δ$$x1=14+14=12$$ Similarly, Δ$$v=12dff2=dvv2+duu2$$⇒$$df(20)2=12(60)2+12(30)2$$⇒$$df=518dff$$×$$100=518$$×$$120$$×$$100=1.39$$%

The lens

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The lens

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1v−1u=1f⇒160+130=1f⇒f=20cmu=x2−x1⇒Δu=Δx2+Δx1=14+14=12 Similarly, Δv=12dff2=dvv2+duu2⇒df(20)2=12(60)2+12(30)2⇒df=518dff×100=518×120×100=1.39%

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