an object of 2 cm height is placed at a distance of 20 cm in front of a convex mirror of focal length 15 cm find the position nature and size of the image thus formed
Answers
Given : An object of 2cm height is placed at a distance of 20cm in front of a convex mirror of focal length 15cm.
To find : The position, nature and size of the image formed.
solution : object distance, u = -20 cm
focal length of convex mirror, f = +15cm
using formula, 1/v + 1/u = 1/f
⇒1/v + 1/-20 = 1/+15
⇒1/v = 1/15 + 1/20 = 4/60 + 3/60
⇒v = + 60/7 cm
Therefore the position of image 60/7 cm from the mirror. positive sign indicates that nature of image is virtual.
now magnification, m = -v/u
⇒height of image/height of object = -v/u
⇒height of image/2cm = -(60/7)/-20
⇒height of image = 3/7 × 2 = 6/7 cm
Therefore the height of image is 6/7 cm. it is clear that size of image is smaller than that of object.
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image distance =150/2 = + 75.5 cm
h=75.5×6