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**Lens**

A lens is a uniform transparent medium bounded between two spherical or one spherical and one plane surface.

**Convex Lens**

A lens which is thinner at edges and thicker at middle is called a convex or converging lens.

**Concave Lens **

A lens which is thicker at edges and thinner at middle, is called a concave or diverging lens.

**Lens Formula**

1/f = 1/v â€“ 1/u

where, f = focal length of the lens, U = distance of object, U = distance of image.

Lens Makerâ€™s formula

1/f=(Î¼ â€“ 1) (1/R_{1} â€“ 1/R_{2})

where, Î¼ = refractive index of the material of the lens and R_{1} and R_{2} are radii of curvature of the lens.

**Power of a Lens**

The reciprocal of the focal length of a lens, when it is measured in metre, is called power of a lens.

Power of a lens, (P)= 1/f(metre)

Its unit is dioptre (D).

The power of a convex (converging) lens is positive and for a concave (diverging) lens it is negative.

**Focal Length of a Lens Combination**

(i) When lenses are in contact 1/F â€“ 1/f_{1} + 1/f_{2}

Power of the combination P = P_{1} + P_{2}

(ii) When lenses are separated by a distance d

1/F = 1/f_{1} + 1/f_{2} â€“ d/f_{1}f_{1}

Power of the combination

P = P_{1} + P_{2} â€“ dP_{1}P_{2}

**Linear Magnification**

m = I/O = v/u

For a small sized object placed linearly along the principal axis, its axial (longitudinal) magnification is given by

Axial magnification = â€“ dv/du = (v/u)^{2}

=(f/f+u)^{2} = (f-v/f)^{2}

**Focal Length of a Convex Lens by Displacement Method**

Focal length of the convex lens f = (a^{2} â€“ d^{2}) / 4a

where, a = distance between the image pin and object pin and

d = distance between two positions of lens.

The distance between the two pins should be greater than four times the focal length of the convex lens, i.e., a > 4f.

Height of the object O = âˆšI_{1}I_{2}

**Cutting of a Lens**

(i) If a symmetrical convex lens of focal length f is cut into two parts along its optic axis, then focal length of each part (a plane convex lens) is 2f. However, if the two parts are joined as shown in figure, the focal length of combination is again f.

(ii) If a symmetrical convex lens of focal length f is cut into two parts along the principal axis, then focal length of each part remains unchanged as f. If these two parts are joined with curved ends an one side, focal length of the combination is f/2. But on joining two 2 parts in opposite sense the net focal length becomes

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