A 6 cm tall object is placed perpendicular to the principal axis of a mirror of focal length distance the object from the mirror is 45 cm. Use mirror formula to determine the position, nature size of the image formed. Also draw labelled ray diagram to show the and image formation in this case.
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Explanation:
Length of the object = 6cm (Given)
Focal length f = -30 cm (Given)
The distance of the object u = -45 cm (Given)
The mirror formula is given as - 1/f = 1/u + 1/v
where f is the the focal length, u is the the image distance and v is the object distance. Thus,
f = 30 cm and v = 45 cm
= 1/u = 1/f - 1/v
= 1/30 - 1/45 = 1/90
= u = 90 cm
Thus, the distance of the image 90cm
Magnification = Image distance/object distance
Magnification = 90/45 = 2
Magnification = image height / object height.
Thus, by substitution -
2 = h/6
h= 6 × 2
= 12
Therefore, the size of the image so formed will be 12 cm.
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