Question

A 4.5 cm needle is placed 25 cm away from a convex mirror of focal length of 15 cm . find the location of image and magnification . also draw a neat ray diagram of it.​

Answer 1

Answer :-

→ Location of the image is 9.375 cm .

→ Magnification is + 0.0375

→ For ray diagram refer to the above attachment.

Explanation :-

We have :-

→ Height of the object (hₒ) = 4.5 cm

→ Distance (u) = 25 cm

→ Focal length (f) = 15 cm

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From sign convention, we have :-

• u = -25 cm

• f = +15 cm

Now, according to mirror formula :-

1/v + 1/u = 1/f

⇒ 1/v = 1/f - 1/u

⇒ 1/v = 1/15 - (-1)/25

⇒ 1/v = (5 + 3)/75

⇒ 1/v = 8/75

⇒ 8v = 75

⇒ v = 75/8

⇒ v = 9.375 cm

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Now, from the formula of magnification of a spherical mirror :-

m = -(v/u)

⇒ m = -(9.375/-25)

⇒ m = -(-0.375)

⇒ m = + 0.375