A point object P (at$$ distance of $$15$$ cm from $$lens) is approaching towards a thin and silvered equiconvex lens of local length $$20$$ cm and refractive index $$1.5$$ with a speed of $$4$$ cms−$$1$$ as shown in figure. Find velocity of image.

Question

A point object P  (at$$ distance of $$15$$ cm from $$lens) is approaching towards a thin and silvered equiconvex lens of local length $$20$$ cm and refractive index $$1.5$$ with a speed of  $$4$$ cms−$$1$$ as shown in figure. Find velocity of image.

Infinity Learn · Accepted Answer

$$1f=($$μ−$$1)(1R+1R)$$ ⇒$$120=(1.5$$−$$1)2R$$ ∴$$R=20cmPower$$ of equivalent mirror is $$P=2P1+Pm=220$$−$$1$$−$$10=110+110=15$$∴−$$1F=15$$ ∴$$F=$$−$$5$$ cm  Combination behaves like Concave Mirror  ∵$$1v+1u=1For1v$$−$$115=$$−$$15$$ Or  $$1v=115$$−$$15=1$$−$$315=$$−$$215$$ ∴$$v=$$−$$152cm$$ ∴$$vimage=$$−$$v2u2dudt=$$−$$($$−$$152)2($$−$$15)2$$×$$4=$$−$$1cms$$−$$1$$

A point object P (at distance of 15 cm from lens) is approaching towards a thin and silvered equiconvex lens of local length 20 cm and refractive index 1.5 with a speed of $4 c m s^{- 1}$ as shown in figure. Find velocity of image.

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A point object P (at distance of 15 cm from lens) is approaching towards a thin and silvered equiconvex lens of local length 20 cm and refractive index 1.5 with a speed of 4 cms−1 as shown in figure. Find velocity of image.

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A point object P (at distance of 15 cm from lens) is approaching towards a thin and silvered equiconvex lens of local length 20 cm and refractive index 1.5 with a speed of $4 c m s^{- 1}$ as shown in figure. Find velocity of image.