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Magnification produced by a convex mirror for a given object of height 5┬аcm is 0.2. Here, the height of the image is ________.
10 cm
5 cm
0.4 cm
1 cm
1 cm
The magnification (m) of a spherical mirror is defined as the ratio of the height of the image (hiтАЛ) to the height of the object (hoтАЛ). Using the formula m=hoтАЛhiтАЛтАЛ, we get 0.2=5┬аcmhiтАЛтАЛ, which gives the height of the image as hiтАЛ=0.2├Ч5┬аcm=1┬аcm.
The magnification (m) of a spherical mirror is defined as the ratio of the height of the image (hiтАЛ) to the height of the object (hoтАЛ). Using the formula m=hoтАЛhiтАЛтАЛ, we get 0.2=5┬аcmhiтАЛтАЛ, which gives the height of the image as hiтАЛ=0.2├Ч5┬аcm=1┬аcm.
Think of looking through a reducing security mirror at a store: a tall person standing in front appears smaller because the mirror produces a diminished image with a magnification less than 1.
HI = M times HO (Height of Image = Magnification ├Ч Height of Object)
m=hoтАЛhiтАЛтАЛ тАФ Magnification in terms of heights
m=тИТuvтАЛ тАФ Magnification in terms of mirror distances
In optics, linear magnification (m) for mirrors determines how much larger or smaller an image is relative to the object. A positive sign of magnification indicates a virtual and erect image, which is always formed by a convex mirror. Since the magnification is 0.2, the image height is a fraction of the object height.
Convex mirrors always form virtual, erect, and diminished images.
The magnification of a convex mirror is always positive and less than 1 (0<m<1).
Object height (hoтАЛ) is always taken as positive above the principal axis.
Provides a wider field of view for drivers as rear-view mirrors.
Does not form real images of real objects under normal conditions.
Rear-view mirrors in automobiles
Security mirrors in shops and blind turns
Option A (10 cm) is incorrect because multiplication by 0.2 would yield 1 cm, not 10 cm.
Option B (1.5 cm) and Option C (0.4 cm) are incorrect arithmetic results.
D is correct тАФ The height of the image is 1 cm.
Always verify signs when dealing with lens and mirror formulas: convex mirrors have positive focal length and magnification between 0 and 1.
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