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General SciencePhysics: Light - Refraction
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An object 3 cm high is placed at a distance of 30 cm from a convex lens of focal length 20 cm. What is the magnification produced?

A

1

B

2

C

2

D

0.5

Correct Answer

ЁЯФм SC тАв Science Concept & PrincipleGeneral SciencePhysics: Light - Refraction
Option B

2

Quick Summary:

The magnification (mmm) for a lens is given by the ratio of image distance (vvv) to object distance (uuu). Using the lens formula, we find the image distance, and subsequently calculate the magnification ratio.

ЁЯФмSCScience SolutionConcept & Principle
ЁЯТб Explanation

The magnification (mmm) for a lens is given by the ratio of image distance (vvv) to object distance (uuu). Using the lens formula, we find the image distance, and subsequently calculate the magnification ratio.

ЁЯТб Everyday Analogy (Real-World Intuition)

A convex lens acts like a magnifying glass; when you move an object close to the focal point, the image flips and enlarges, just like how a camera lens focuses light onto a sensor.

ЁЯФв Key Formulas

1f=1vтИТ1u\frac{1}{f} = \frac{1}{v} - \frac{1}{u}f1тАЛ=v1тАЛтИТu1тАЛ тАФ Lens Formula

m=vu=hihom = \frac{v}{u} = \frac{h_i}{h_o}m=uvтАЛ=hoтАЛhiтАЛтАЛ тАФ Magnification Formula

тЪЩя╕П Working Principle

The lens formula is 1f=1vтИТ1u\frac{1}{f} = \frac{1}{v} - \frac{1}{u}f1тАЛ=v1тАЛтИТu1тАЛ. With f=+20┬аcmf = +20 \text{ cm}f=+20┬аcm and u=тИТ30┬аcmu = -30 \text{ cm}u=тИТ30┬аcm (sign convention), we get 1v=120+1тИТ30=3тИТ260=160\frac{1}{v} = \frac{1}{20} + \frac{1}{-30} = \frac{3-2}{60} = \frac{1}{60}v1тАЛ=201тАЛ+тИТ301тАЛ=603тИТ2тАЛ=601тАЛ. Thus, v=60┬аcmv = 60 \text{ cm}v=60┬аcm. Magnification m=vu=60тИТ30=тИТ2m = \frac{v}{u} = \frac{60}{-30} = -2m=uvтАЛ=тИТ3060тАЛ=тИТ2. Note: The question implies magnitude or uses specific conventions; however, purely calculation-wise, m=тИТ2m = -2m=тИТ2. Given the options, there is an error in the provided answer key as the correct value is тИТ2-2тИТ2.

ЁЯУМ Key Points
  • тЦ╕

    For a convex lens, if f<u<2ff < u < 2ff<u<2f, the image formed is real, inverted, and magnified.

  • тЦ╕

    Sign convention: uuu is negative, fff is positive for convex lenses.

  • тЦ╕

    A magnification of тИТ2-2тИТ2 indicates the image is inverted and twice the size of the object.

тЬЕ Advantages
  • тЦ╕

    Provides clear magnification ratios for optical design.

тЭМ Disadvantages / Limitations
  • тЦ╕

    Standard lens formula assumes thin lens approximation.

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Camera lenses

  • тЦ╕

    Microscopes

ЁЯУД Additional Information
  • тЦ╕

    The provided answer '1' is mathematically incorrect based on the given parameters u=30u=30u=30 and f=20f=20f=20.

  • тЦ╕

    At u=2fu = 2fu=2f (i.e., 40┬аcm40 \text{ cm}40┬аcm), the magnification would be тИТ1-1тИТ1, leading to a magnitude of 111.

ЁЯУК Diagram / Illustration
Magnification by Convex Lens 1 Given Data (Sign Convention) f = +20 cm, u = -30 cm, hтВТ = 3 cm 2 Lens Formula Calculation 1/v = 1/f + 1/u = 1/20 - 1/30 = 1/60 тЯ╣ v = 60 cm 3 Magnification Formula m = v / u = 60 / -30 = -2 4 Result Interpretation Magnification (m) = -2 (Magnitude = 2) Final Answer: Magnitude of Magnification = 2
тЬЕ

B is correct тАФ Using the lens formula, the magnification is calculated to be -2, implying the magnitude is 2.

Core Concepts Used
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Lens Formula Magnification Sign Convention
ЁЯТб EXAM TIP

Always verify the sign of uuu as negative in lens problems; ignoring this is the most common cause of calculation errors in competitive exams.

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