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A convex lens of focal length 10 cm is placed at a distance of 60 cm from a screen. How far from the lens should an object be placed so as to obtain a real image on the screen?

Refraction Lens

ICSE 2023

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Answer

Given, focal length = 10 cm

Image distance (v) = 60 cm

Object distance (u) = ?

From lens formula —

1v−1u=1f\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f} \\[1em]

Substituting the values in the formula we get,

160−1u=110⇒160−110=1u⇒1−660=1u⇒−560=1u⇒1u=−112⇒u=−12\dfrac{1}{60} - \dfrac{1}{\text{u}} = \dfrac{1}{10} \\[1em] \Rightarrow \dfrac{1}{60} - \dfrac{1}{10} = \dfrac{1}{\text{u}} \\[1em] \Rightarrow \dfrac{1 - 6}{60} = \dfrac{1}{\text{u}} \\[1em] \Rightarrow \dfrac{-5}{60} = \dfrac{1}{\text{u}} \\[1em] \Rightarrow \dfrac{1}{\text{u}} = \dfrac{-1}{12} \\[1em] \Rightarrow u = -12

∴ The object should be placed at a distance of 12 cm in front of the lens.

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