At what distance from a concave mirror of focal length 10 cm should an object 2 cm long be placed in order to get an erect image 6 cm tall?

By Ritesh|Updated : November 8th, 2022

At a -6.7 cm distance from a concave mirror of focal length 10 cm should an object 2 cm long be placed in order to get an erect image 6 cm tall. Steps to calculate the distance from a concave mirror of focal length:

Step 1: Given parameters

Height of the object, h0 = 2 cm

The focal length of the concave mirror, f = - 10 cm

Height of the image, hi = 6 cm

Step 2: Now we have to calculate Parameter

We need to find the distance of the object

Step 3: The formula to find the distance of the object is

m = hi/ho and 1/v + 1/u = 1/f

Step 4: calculation of the distance of the object is

Thus, m = 3 cm (erect image)

Also m = -v/u

We get v = - 3u

Using the Mirror formula,

1/v + 1/u = 1/f

1/(-3u) + 1/u = 1/f

Hence, u = -6.70 cm

Therefore, the object must be placed in a -6.7 cm concave mirror to get an image of 6 cm tall.

Concave Mirror Image Formation

Different kinds of images can be created by shifting the object's position in the concave mirror. When the object is positioned, various images are created:

  1. At the infinity
  2. Beyond the centre of curvature
  3. At the centre of curvature
  4. Between the centre of curvature and the principal focus
  5. The principal focus
  6. Between the principal focus and pole

Summary:

At what distance from a concave mirror of focal length 10 cm should an object 2 cm long be placed in order to get an erect image 6 cm tall?

An object 2 cm long should be placed at a distance of -6.7 cm from a concave mirror with a focal length of 10 cm in order to obtain an upright image of 6 cm tall. The formula to determine the object distance is m = hi/ho and 1/v + 1/u = 1/f.

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