Light – Lens Formula and Power of a Lens

Lens formula is similar to Mirror formula except that the +ve sign is replaced by -ve sign.  The power of a Lens is the power of our spectacles.

LENS FORMULA

(i)  We have formula for spherical lenses. This formula gives the relationship between object distance (u), image-distance (v) and the focal length (f ). The lens formula is expressed as

Lens Formula

(ii)  The lens formula given above is general and is valid in all situations for any spherical lens. Take proper care of the signs of different quantities, while putting numerical values for solving problems relating to lenses.

MAGNIFICATION BY A LENS

(i)  The magnification (m) produced by a lens is defined as the ratio of the height of the image and the height of the object. It is represented by:

Magnification_001

(ii)  Magnification produced by a lens is also related to the object-distance u, and the image-distance v. It is given by: 

Magnification_002

POWER OF A LENS

(i)  The degree of convergence or divergence of light rays by a lens is termed as power of the lens.

(ii)  The power of a lens is defined as the reciprocal of its focal length. It is represented by the letter P. The power P of a lens of focal length f is given by:

Power of a Lens

(iii)  The SI unit of power of a lens is ‘dioptre’. It is denoted by the letter D. If f is expressed in metres, then, power is expressed in dioptres.

(iv)  1 dioptre is the power of a lens whose focal length is 1 metre. 1D = 1m–1.

(v)  You may note that the power of a convex lens is positive and that of a concave lens is negative.

(vi)  Opticians prescribe corrective lenses indicating their powers. Let us say the lens prescribed has power equal to + 4.0 D. This means the lens prescribed is convex. The focal length of the lens is + 0.25 m. Similarly, a lens of power – 2.0 D has a focal length of – 0.50 m. The lens is concave.

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