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When an object is placed at a distance of 60 cm from a diverging spherical mirror magnification produces is 0.5 where should the object be placed to get a magnification 1 /3?
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Given:

  • Distance of the object from the mirror, u = 60 cm

  • Magnification produced, m = 0.5

  • Magnification required, m' = 1/3



To Find:

  • The distance of the object from the mirror for the required magnification.



Explanation:

  • When an object is placed at a distance of 60 cm from a diverging spherical mirror, magnification produced is 0.5.

  • Magnification is the ratio of the height of the image to the height of the object.

  • m = (-v/u) where v is the distance of the image from the mirror.

  • For the given situation, we can find the distance of the image from the mirror using the magnification equation.

  • m = -v/u

  • 0.5 = -v/60

  • v = -30 cm

  • As the image is formed behind the mirror, the distance of the image is negative.

  • Now, we need to find the distance of the object for the required magnification.

  • For a diverging mirror, the magnification is negative.

  • m' = (-v'/u)

  • 1/3 = (-v'/u)

  • v' = -u/3

  • As the image is formed behind the mirror, the distance of the image is negative.

  • Substituting the values, we get:

  • -30 = (-u/3)/0.5

  • -30 = -u/1.5

  • u = 45 cm

  • Therefore, the object should be placed at a distance of 45 cm from the mirror to get a magnification of 1/3.

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When an object is placed at a distance of 60 cm from a diverging spherical mirror magnification produces is 0.5 where should the object be placed to get a magnification 1 /3?
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