Q.
A 4.5cm needle is placed 12cm away from a convex mirror of focal length 15cm. Give the location of the image and the magnification. What happens as the needle is moved farther from the mirror?
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Ray Optics and Optical Instruments
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Solution:
Given, focal length of convex mirror f=+15cm
(Focal length of convex mirror is taken as positive)
Distance of object u=−12cm
Size of object O=4.5cm
Using the mirror formula, f1=v1+u1 151=v1−121 ⇒v1=151+121 =604+5=609
Distance of image from the mirror v=6.7cm T
he positive sign shows that the image is formed behind the mirror.
Using the formula of magnification, m=−uv=O1 −12−6.7=4.51
Size of image I=2.5cm
As I is positive, so image is erect and virtual.
Magnification m is given by m=O1=4.52.5=4525=95
As the needle moves away from the mirror, the image also moves away from the mirror (as u→∞,v→f) and the size of image goes on decreasing.