Question

An object of length 4 cm is placed in front of a concave mirror at distance 30 cm. The focal length of mirror is 15 cm. (a) Where will the image form? (b) What will be the length of image?

Answer 1

the image will form at c (center of curvature) and the length of image will be equal to that of the object

Answer 2

Given:

• Height of image = 4cm
• Object distance = -30cm
• Focal length = -15cm

To find:

• Where the image will form.
• Length of the image.

Solution:

❐ Using mirror formula,

• 1/f = 1/v + 1/u

⇒ 1/v = 1/f - 1/u

⇒ 1/v = 1/-15 - 1/30

⇒ 1/v = 1/30 - 1/15

⇒ 1/v = -1/30

⇒ v = -30cm

Hence, the image is formed at a distance of 30cm in front of the mirror.

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❐ Using magnification formula,

• m = hᵢ/hₒ = -v/u

⇒ hᵢ/4 = -(-30)/-30

⇒ hᵢ/4 = -1

⇒ hᵢ = -1 × 4

⇒ hᵢ = -4cm

Hence, the length of the image is 4cm.

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