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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Geometrical Optics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Geometrical Optics

A 5.0 diopter lens produces a virtual image which is 4 times the...

A

5.0

diopter lens produces a virtual image which is

4

times the object placed perpendicularly on the principal axis of the lens. Determine the distance of the object from the lens.

Options

A $25\text{ cm}$
B $60\text{ cm}$
C $15\text{ cm}$
D $20\text{ cm}$

Correct answer

C. $15\text{ cm}$

Step-by-step solution

Power of the lens,

P = 5.0 \text{ D}

Focal length,

f = \dfrac{100}{P} = \dfrac{100}{5} = 20 \text{ cm}

Since the lens forms a virtual and magnified image, the magnification is

m = +4

.

Using the relation

m = \dfrac{v}{u}

, we get

v = 4u

.

Applying the lens formula:

\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}

\dfrac{1}{4u} - \dfrac{1}{u} = \dfrac{1}{20}

\dfrac{1 - 4}{4u} = \dfrac{1}{20}

\dfrac{-3}{4u} = \dfrac{1}{20}

4u = -60 \Rightarrow u = -15 \text{ cm}

The distance of the object from the lens is

15 \text{ cm}

.

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