JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Geometrical Optics

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The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of convex lens is ____ cm.

Answer: 15

Solution

For a thin lens the magnification at object distance

u

has magnitude

∣ m ∣ = \frac{f}{f + u}

Equal image size at

u = - 20

cm and

u = - 10

cm requires

\frac{f}{f - 20} = \frac{f}{f - 10} \Rightarrow ∣ f - 20∣ = ∣ f - 10∣

The two brackets cannot be equal with the same sign, so

20 - f = f - 10

, giving

f = 15

cm. At

u = - 20

cm the image is then real with

m = - 3

and at

u = - 10

cm it is virtual with

m = + 3

, both three times the object.

The focal length of the convex lens is

15

cm.

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Numerical answer

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