Join 60,000+ competitive exam aspirants
An object of height 30┬аcm is placed in front of a concave lens and an image of height 10┬аcm is formed. The magnification of the lens is:
1/3
тИТ20
3
20
1/3
Magnification for a lens is defined as the ratio of the height of the image to the height of the object. Since hiтАЛ=10 cm and hoтАЛ=30 cm, the magnification is m=3010тАЛ=31тАЛ.
Magnification for a lens is defined as the ratio of the height of the image to the height of the object. Since hiтАЛ=10 cm and hoтАЛ=30 cm, the magnification is m=3010тАЛ=31тАЛ.
Think of looking through a peephole or a concave lens at a tall object; the object appears smaller than it actually is. The 'magnification' in this case tells you what fraction of the original size the image has become.
m=hoтАЛhiтАЛтАЛ тАФ Magnification formula based on heights
m=uvтАЛ тАФ Magnification formula based on distances
In optics, the linear magnification (m) of a lens is given by the formula m=hoтАЛhiтАЛтАЛ, where hiтАЛ is the height of the image and hoтАЛ is the height of the object. For a concave lens, the image formed is always virtual, erect, and diminished, meaning the image height is always less than the object height, resulting in a magnification value between 0 and 1.
Concave lenses always form virtual, erect, and diminished images.
For a concave lens, magnification (m) is always positive and less than 1 (0<m<1).
Magnification is a unitless ratio.
Used in diverging light rays for corrective eyewear (myopia).
Spectacles for nearsightedness
Peepholes in doors
The sign convention for concave lenses results in a positive m because the image is erect (both hiтАЛ and hoтАЛ are positive in the Cartesian sign convention).
Option B (-20), C (3), and D (20) are incorrect as they do not represent the correct ratio of 10/30.
A is correct тАФ The magnification m is the ratio of image height (hiтАЛ) to object height (hoтАЛ), which equals 30┬аcm10┬аcmтАЛ=31тАЛ.
Always check sign conventions in lens problems; for virtual images formed by concave lenses, hiтАЛ and hoтАЛ are both measured upwards from the principal axis, keeping magnification positive.