# Lens

Lens is a transparent medium bounded by two refracting surfaces such that at least one surface is curved. Curved surface can be spherical, cylindrical, etc.

Lenses are of two basic types: convex, which are thicker in the middle than at the edges, and concave, for which the reverse holds.

**Fig. 19**

- As there are two spherical surfaces, there are two centers of curvature
*C*_{1}and*C*_{2}and correspondingly two radii of curvature*R*_{1}and*R*_{2} - The line joining
*C*_{1}and*C*_{2}is called the principal axis of the lens. The center of the thin lens which is on the principal axis is called the optical center. - A ray passing through optical center proceeds undeviated through the lens.

**Fig. 20**

**Principal focus**We define two principal focii for the lens. We are mainly concerned with the second principal focus (

*F*). Thus, wherever we write the focus, it means the second principal focus.

**First principal focus:**An object point for which image is formed at infinity.

**Fig. 21**

**Second principal focus:**An image point for an object at infinity.

**Fig. 22**

# Focal Length, Power, and Aperture of Lens

**Focal length (**Distance of second principle focus from optical center is called focal length.

*f*)*f*

_{convex}→ positive,

*f*

_{concave}→ negative,

*f*

_{plane}→ ∞

**Aperture**Effective diameter of light-transmitting area is called aperture. Intensity of image ∝ (Aperature)

^{2}

**Power of lens (**The ability of a lens to deviate the path of the rays passing through it. If the lens converges the rays parallel to the principal axis its power is positive and if it diverges the rays it is negative. Power of lens,; Unit of power is Diopter (

*P*)*D*)

*P*

_{convex}→ positive,

*P*

_{concave}→ negative,

*P*

_{plane}→ zero

# Lens Maker’s Formula and Lens Formula

**Lens maker’s formula**If

*R*

_{1}and

*R*

_{2}are the radii of curvature of first and second refracting surfaces of a thin lens of focal length

*f*and refractive index

*μ*(wrt surrounding medium) then the relation between

*f*,

*μ*,

*R*

_{1}, and

*R*

_{2}is known as lens maker’s formula.

**Lens formula**The expression which shows the relation between

*u*,

*v*, and

*f*is called lens formula.