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An object is placed a distance of twice the focal length away from a diverging lens. What is the magnification of the image?

-1/3
+1/3
-2/3
-3/2
+2/3
+3/2

Respuesta :

skyluke89

Answer:

+1/3

Explanation:

The lens equation states that:

[tex]\frac{1}{f}=\frac{1}{p}+\frac{1}{q}[/tex]

where

f is the focal length

p is the distance of the object from the lens

q is the distance of the image from the lens

For a diverging lens, the focal length is negative: [tex]f=-f[/tex]

and we also know that the object is placed a distance of twice the focal length, so [tex]p=2f[/tex]

So we can find q from the equation above

[tex]\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{-f}-\frac{1}{2f}=-\frac{3}{2f}\\q=-\frac{2}{3}f[/tex]

And the magnification of the image is given by

[tex]M=-\frac{q}{p}=-\frac{-\frac{2}{3}f}{2f}=\frac{1}{3}[/tex]

johanrusli

The magnification of the image is -⅓

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Further explanation

We will solve this problem using following formula:

[tex]\boxed {\frac{1}{s_o} + \frac{1}{s_i} = \frac{1}{f}}[/tex]

[tex]\boxed {M = s_i \div s_o}[/tex]

where:

so = distance of object from lens

si = distance of image from lens

f = focal length of lens

M = magnification of lens

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Given:

focal length of diverging lens = -f

distance of object from lens = so = 2f

Asked:

magnification of the image = M = ?

Solution:

Firstly , we will find the distance of image from lens as follows :

[tex]\frac{1}{s_o} + \frac{1}{s_i} = \frac{1}{f}[/tex]

[tex]\frac{1}{2f} + \frac{1}{s_i} = \frac{1}{-f}[/tex]

[tex]\frac{1}{s_i} = - \frac{1}{f} - \frac{1}{2f}[/tex]

[tex]\frac{1}{s_i} = - \frac{3}{2f}[/tex]

[tex]\boxed {s_i = - \frac{2}{3} f}[/tex]

[tex]\texttt{ }[/tex]

Next , we could calculate the magnification of the lens as follows :

[tex]M = s_i \div s_o[/tex]

[tex]M = - (\frac{2}{3} f) \div ( 2f )[/tex]

[tex]\boxed {M = - \frac{1}{3}}[/tex]

[tex]\texttt{ }[/tex]

Conclusion :

The magnification of the image is -⅓

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Learn more

  • Compound Microscope : https://brainly.com/question/7512369
  • Reflecting Telescope : https://brainly.com/question/12583524
  • Focal Length : https://brainly.com/question/8679241
  • Mirror an Lenses : https://brainly.com/question/3067085

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Answer details

Grade: High School

Subject: Physics

Chapter: Light - Diverging Lens

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