A4.5 cm needle is placed 12 cm away from a convex mirror of focallength 15 cm. Give the location of the image and the magnification.Describe what happens as the needle is moved farther from the mirror.

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Solution

Heightof the needle, h₁= 4.5 cm
Objectdistance, u =−12 cm
Focallength of the convex mirror, f= 15 cm
Imagedistance = v
Thevalue of v canbe obtained using the mirror formula:
Hence,the image of the needle is 6.7 cm away fromthe mirror. Also, it is on the other side of the mirror.
Theimage size is given by the magnification formula:
Hence,magnification of the image,
Theheight of the image is 2.5 cm. The positivesign indicates that the image is erect, virtual, and diminished.
Ifthe needle is moved farther from the mirror, the image will also moveaway from the mirror, and the size of the image will reducegradually.

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