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Question

(a) Draw a diagram to represent a convex mirror. On this diagram mark principal axis, principal focus F and the centre of curvature C if the focal length of convex mirror is 3 cm.
(b) An object 1 cm tall is placed 30 cm in front of a convex mirror of focal length 20 cm. Find the size and position of the image formed by the convex mirror.

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Solution

(a) Ray Diagram-

(b) Given,
The mirror is a diverging mirror, i.e. convex mirror.
Height of the object 'ho' = 1 cm
Distance of the object from the mirror 'u' = -30 cm
Focal length of the convex mirror 'f' = 20 cm
We have to find the position of the image 'v', height of the image 'hi' and its magnification 'm'.
Using the mirror formula, we get
1f=1v+1u120=1v+1-30130+120=1v260+360=1v560=1v v=605=12 cm

The image will be at a distance of 12 cm behind the mirror .
Now, using the magnification formula, we get
m=-vum=-12-30=0.4
Thus, the image is virtual, erect and smaller in size.
Also,
m=hiho0.4=hi1hi=0.4cm
Therefore, the height of the image is 0.4 cm.

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