Math, asked by MichWorldCutiestGirl, 7 hours ago

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An object 5 cm in size is placed at 12 CM in front of a concave mirror of radius of curvature of 20 CM at what distance from the mirror should a screen be placed in order to obtain a sharp image? find the nature and size of the L.


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Answers

Answered by Aryan0123
45

Answer:

☞ Nature of image:

  • Real
  • Inverted
  • Enlarged

☞ Size of image = - 25 cm

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Step-by-step explanation:

Given:

  • Object size = 5 cm
  • Concave mirror
  • Object-mirror distance = u = - 12 cm
  • Radius of curvature = R = 20 cm

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To find:

Nature and size of image

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Solution:

First let's find the focal length (f)

R = 2f

⇒ f = R/2

⇒ f = 20/2

⇒ f = 10 cm

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Hence, Focal length = -10 cm

(Negative sign because it is a concave mirror)

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Applying mirror formula,

 \red{\bold{\dfrac{1}{v}  +  \dfrac{1}{u}  =  \dfrac{1}{f} }} \\  \\

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

 \implies \sf{ \dfrac{1}{v} =  \dfrac{1}{ -  10}  -  \dfrac{1}{ - 12} } \\  \\

 \implies \sf{ \dfrac{1}{v}  =  \dfrac{ - 1}{10} +  \dfrac{1}{12} } \\  \\

 \implies \sf{ \dfrac{1}{v}  =  \dfrac{1}{12}  -  \dfrac{1}{10} } \\  \\

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Taking LCM and solving,

\implies \sf{ \dfrac{1}{v}  =  \dfrac{5 - 6}{60} } \\  \\

\implies \sf{ \dfrac{1}{v}  =  \dfrac{ - 1}{60} } \\  \\

 \therefore \:  \bf{v =  - 60 \: cm} \\  \\

So, the screen must be placed at a distance of 60 cm in front of the mirror to obtain a sharp image.

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Now, let's find it's magnification.

\pink{\bf{m =  \dfrac{ - v}{u} } }\\  \\

\implies \:  \sf{m =  \dfrac{ - ( - 60)}{ - 12} } \\  \\

\implies \sf{m =  \dfrac{ - 60}{12} } \\  \\

\implies \boxed{\sf{m =  - 5}} \\  \\

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Magnification is in negative. So, the image is real and inverted.

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Modulus of magnification = |m| = 5

5 > 1

So, the image is enlarged.

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∴ Nature of image:

  • Real
  • Inverted
  • Enlarged

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Also,

 \green{ \sf{m =  \dfrac{Height_{(image)}}{Height_{(object)}} }} \\  \\

 \implies \sf{ - 5 =  \dfrac{Height_{(image)}}{5} } \\  \\

 \implies \boxed{ \sf{Height_{(image)} =  - 25 \: cm}} \\  \\

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Some TIPS to find nature of image from magnification:

⭐ If magnification is positive, image is virtual and erect

⭐ If magnification is negative, image is real and inverted

⭐ If modulus of magnification is greater than 1, then the image is enlarged

⭐ If modulus of magnification is lesser than 1, then the image is diminished

⭐ If modulus of magnification = 1, image is same size of the object.

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