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Question

A point object is placed at a distance of 30cm from a convex mirror of focal length of 30cm. The image will form at________


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Solution

Step 1. Given data

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  1. According to the sign convention in mirror, the object distance u=-30cm,
  2. Focal length f=30cm
  3. We have to find image distance v.

Step 2. Formula to be used.

Mirror formula:

  1. A mirror can be made by silvering a metal surface with glass in front and paint at its back.
  2. The mirror formula represent the relation between focal length, image distance and object distance,

1f=1u+1v

Here, f is focal length, v is the distance of the image from the mirror and u is the distance of the object from the mirror.

Step 3. Calculate the image distance.

Now, by using the mirror formula, we get,

130=1-30+1v

1v=130+130

1v=230

2v=30

v=15

  1. The sign obtained is positive and the image distance is 15cm.
  2. According to the sign convention in mirror, the image is formed 15cm behind the mirror.

Hence, A point object is placed at a distance of 30cm from a convex mirror of focal length of 30cm. The image will form at 15 cm behind the image.


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