An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of a focal length of 18 cm. At what distance from the mirror should a screen be placed so that a sharply focused image can be obtained? Find the size and the nature of the image.

By Ritesh|Updated : November 11th, 2022

The size of the image is 14 cm and is a magnified image. Steps to find the size and the nature of the image:

Step (1) Given that:

Focal length, f = -18 cm (Focal length of a concave mirror is taken negatively)

The object distance, u = -27 cm (object distance should be taken negatively)

Object size, h0 = 7.0 cm

Step (2) Now we have to find the image distance using the mirror formula:

We know that the mirror formula:

1/v = 1/f - 1/u

Now substituting the values we get:

1/v = -1/18 + 1/27 = -1/54

In simplification we get the:

v = -54 cm

The mirror should be put in front of the screen at a distance of 54 cm.

Step (3) Now we have to find the size of the image:

hi/ho = v/u

Now substituting the values we get:

hi/7 = -54/-27

In simplification we get the:

hi = 2 x 7 = 14 cm

As a result, the image is 14 cm long and is enlarged.

Characteristics of Concave Mirror

  • When it hits and reflects back from the concave mirror's reflecting surface, light converges at a single point.
  • This is why it is sometimes referred to as a converging mirror.
  • A magnified, upright, and virtual image can be obtained when the concave mirror is positioned very close to the item.
  • The size of the image, however, decreases as the distance between the item and the mirror increases, creating a true and inverted image instead.
  • The concave mirror can produce a little or huge, real or virtual image.

Summary:

An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of a focal length of 18 cm. At what distance from the mirror should a screen be placed so that a sharply focused image can be obtained? Find the size and the nature of the image.

An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of a focal length of 18 cm. At 14 cm from the mirror should a screen be placed so that a sharply focused image can be obtained. The size of the image is 14 cm and is a magnified image.

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