JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Geometrical Optics

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The distance between object and its two times magnified real image as produced by a convex lens is 45 cm. The focal length of the lens used is ______ cm.

Answer: 10

Solution

For a real, twice-magnified image,

m = - 2

, so

v = - 2 u

.

Given

∣ v - u ∣ = 45

∣ - 2 u - u ∣ = 45 \Rightarrow 3∣ u ∣ = 45 \Rightarrow u = - 15 cm, v = 30 cm

\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{30} + \frac{1}{15} = \frac{1}{10} \Rightarrow f = 10 cm

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Integer answer

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