Tuesday, January 27, 2015

Refraction of Light Through Curved Surfaces

Sign convention

The rules of refraction of the light through curved surfaces are different from the rules of the refraction of the light through a plain surface. Optic Centre of the curved surface is taken as reference to measure all the distances. The incident light is always considered from left to right in the given diagram. 

If the object distance and the image distance are measured along the direction of incident light, they are treated like positive values. If the distance of the object or image is measured against the direction of the incident light, it shall be treated as negative. This is called sign convention. Throughout the Ray optics,we are going to follow the same sign convention.

Law of refraction of the light at the curved surfaces is represented as shown in the attached diagram.

A lens is a piece of a transparent material which has two refracting surfaces such that at least one of them is curved. The refractive index of the lens material shall be different from the surroundings refractive index.

There are different types of lenses like double convex lens, Plano convex lens, double concave lens and Plano concave lens. The double convex lens consists of two convex surfaces whereas the Plano convex lens consists of only one convex surface. The double concave lens consists of two concave surfaces and the plano concave lens consists of only one concave surface.

While solving all the problems that are relevant to lens, we assume that light is falling from left to the right in the given diagram or in a given situation. This is a default way of consideration and it is called sign convention. In the lens formula or in the lens makers formula, we shall write the known values with the sign convention. The known values have to be written as it is that are there in the formula without applying the sign convention. The answer will decide the corresponding sign convention.

Any curved portion of the lens is drawn from a sphere. The radius of the corresponding sphere is called radius of curvature. Radius of curvature is mathematically double to the value of the focal length. The light rays after passing through the lens will converge at a particular point and that particular point is called principal focus. The distance between optics Centre and the principal focus is called focal length. The radius of curvature that is measured along the direction of the incident light is treated as positive and vice versa.

To know the relation between object distance, image distance and the focal length of a lens we are having a formula called Lens formula.

To make a lens with a particular focal length, we can use a formula called lens makers formula. The focal length of a lens depends on the refractive index of the material of the lens, refractive index of the surroundings of the medium and the radius of curvature of the curved surfaces. For a plain surface the radius of curvature is infinite.

We can write the lens makers formula for the concave lens as shown.

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