Question

An object of height 1.5 cm is placed on the axis of
a convex lens of focal length 25 cm. A real image
is formed at a distance of 75 cm from the lens.
The size of the image will be
(a) 4.5 cm
(b) 3.0 cm
(C) 0.75 cm
(d) 0.5 cm
C
D
A
B​

Answer 1

GiveN :

• Focal length, f = 25 cm

• Height of the object, hi = 1.5 cm

• Image distance, v = 75 cm

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We've to find out the Size of the image formed.

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By using lens formula :

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$\longrightarrow\sf\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$

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$\longrightarrow\sf \dfrac{1}{u} = \dfrac{1}{v} - \dfrac{1}{f}$

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$\longrightarrow\sf \dfrac{1}{u} = \dfrac{1}{75} - \dfrac{1}{25}$

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$\longrightarrow\sf \dfrac{1}{u} = \dfrac{1 - 3}{75}$

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$\longrightarrow\sf \dfrac{1}{u} = \dfrac{ - 2}{75}$

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$\longrightarrow\sf u = \dfrac{ - 75}{ 2}$

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Now, we'll calculate the magnification & Size of the image.

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$\longrightarrow\sf m = \dfrac{u}{v}$

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$\longrightarrow\sf m =\dfrac {75 \times 2 }{75}$

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$\longrightarrow\sf m = 2$

Hence,

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$\therefore$ Size of the image = 1.5 × 2 = 3 cm. [Option b]