Question

A 2.0 cm tall object is placed perpendicular to the principal axis of a concave mirror of focal length 10 cm. The distance of the object from the mirror is 15 cm. Find the nature, position and size of the image formed. Represent the situation with the help of a ray diagram.​

Answer 1

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✏️ Answer:-

★ Image distance, v = -30.0 cm

★ Size of the image, h' = - 4 cm

★ Nature of the image formed– Real, inverted and enlarged.

✏️ Explanation:-

★ Given:-

• Focal length, f = -10 cm;

• Object distance, u = -15 cm; and

• Height of the object, h = +2.0 cm

★ To find:-

• Image distance, v;

• Size of the image, h' and;

• Nature of the image.

★ Solution:-

• Using the mirror formula, we have,

1/v + 1/u = 1/f

On plugging in the values, we get,

1/v + 1/-15 = 1/-10

⇒1/v = 1/15 - 1/10

⇒v = -30.0 cm

∴ The image is formed at a distance of 30 cm in front of the mirror.

Magnification,

m = h'/h = -v/u

⇒h' = -h × v/u

⇒h' = -2 × -30/-15

⇒h' = - 4 cm

Hence, the size of the image is 4 cm. The -ve sign denotes that the image formed is inverted and real.

Thus, nature of the image formed would be real, inverted and enlarged.

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I hope this helps! :)