Refraction of Light

Optical Centre

It is the centre of a lens. It is denoted by the letter O. A ray of light passing through the optical centre of a lens does not suffer any deviation. It is also referred to as optic centre.

Principal Axis

Principal axis is the straight line joining the centres of curvatures of the two curved surfaces of a lens.

Principal Foci

Rays of light can pass through the lens in any direction and hence there will be two principal foci on either side of the lens and they are referred to as the first principal focus and the second principal focus of a lens.

First Principal Focus (F₁)

It is a point on the principal axis of the lens such that the rays of light starting from it (convex lens) or appearing to meet at the point (concave lens) after refraction from the two surfaces of the lens become parallel to the principal axis of the lens.

The distance from the optic centre to the first focus is called the first focal length (f₁) of the lens.

Second Principal Focus (F₂)

It is a point on the principal axis of the lens such that the rays of light parallel to the principal axis of the lens after refraction from both the surfaces of the lens pass through this point (convex lens) or appear to be coming from this point (concave lens).

The distance from the optic centre to the second principal focus is called the second focal length (f₂) of the lens.

If the medium on both sides of the lens is same then the first and the second focal lengths will be equal.

Focus of a convex lens is real whereas that of the concave lens is virtual.

Sign Convention for Spherical Lenses

• All distances are measured from the optical centre of the lens.
• The distances measured in the direction of the incident light are taken as positive and the distances measured in the direction opposite to the direction of incident  light are taken as negative.
• All measurements made above the principal axis are taken as positive and the measurements made below the principal axis are taken as negative, i.e., object height is always taken as positive and the image height is positive only for virtual image.

Note

The focal length of a convex lens is always positive and that of a concave lens in always negative.