Question

A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm .Give the location of the image and determine the magnification.

Answer 1

15÷12=1.25 magnification

Answer 2

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Given: Height of the needle, H_{1}H

1

= 4.5cm.

Object distance, u= −12cm.

The focal length of the convex mirror, f=15cm.

Image distance, v The value of v can be obtained using the mirror formula.

v/1 + u/1 = f/1

1/v + 1/-12 = 1/15

v/1= 12/1 + 151

v1=609

∴ v ≈ 6.7cm

Hence, the image of the needle is 6.7 cm away from the mirror. Also, it is on the other side of the mirror.

The image size is given by the magnification formula.

m = h′/h = −v/u

h′ = $\frac{6.7*4.5}{12}$

12

6.7∗4.5

⇒ h′ = +2.5cm

So, m = \frac{2.5}{4.5}

4.5

2.5

m = 0.56

The height of the image is 2.5cm. The positive sign indicates that the image is erect, virtual, and diminished. If the needle is moved farther from the mirror, the size of the image will reduce gradually.

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