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Question

A 4.5 cm needle is placed at 12 cm away from a convex mirror of a focal length of 15cm.

a) Give the location of the image and the magnification.

b) Explain what will happen if the needle is moved farther away from the mirror.


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Solution

a)Step 1: Given data.

Height of object (ho) = 4.5 cm.

Object distance (u) = -12 cm ( negative sign because of Cartesian sign convention)

Focal length of the mirror (f) = 15 cm.

Step 2: Finding the image distance.

1. According to mirror formulae

,1f=1u+1vvimagedistance

. 1v=1f-1u=115-1-12=115+112=27180=320v=203=6.7cm

Hence the location of the image is 20 cm in the back of the mirror.

Step 3: Calculating the magnification and size of image.

1. Magnification,M=hiho=-VUM=-6.7-12=0.56

2. M=hiho=0.56hi=0.56×ho=0.56×4.5=2.52cm

Size of image = 2.52 cm

b) Explanation: The image distance also increases with the object distance, and size of the image will reduce with an increase in object distance.


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