Refraction from a Spherical Surface

A lens is a homogeneous transparent medium such as glass bounded by two curved surfaces or one curved and one plane surface. The curved surface may be cylindrical, paraboloidal or spherical, but most surfaces are spherical. A simple lens is made up of just one transparent element, whereas a compound lens is made up of several simple lenses that are all aligned along the same axis. Refraction from a spherical surface occurs among two clear mediums as well. At any point on the spherical surface, the laws of refraction apply. At the point of incidence, the normal is parallel to the tangent plane and to the spherical surface. As a result, the normal usually travels through the curvature’s centre. Research on refraction from spherical surfaces leads to a better understanding of narrow lenses, which have two surfaces, one or both of which must be spherical.

Types of Spherical Lenses

Lenses can be of many types, some of them as stated below:

• Convex Lens: A convex lens is one in which the centre is thicker than the edges. 
• Concave Lens: When the centre of the lens is thinner than its rims, it is called a concave lens.
• Meniscus Lens: A meniscus lens has one concave side and the other side that is convex.
• Plano Lens: A flat lens is referred to as a Plano lens. When one end is flat and the other is concave or convex, this term is used. A flat is sometimes known as a “plain.”

Types of Refraction from Spherical Surfaces 

The refraction at the spherical surface is of two types:

• Convex Spherical Refracting Surface, which is convex towards the rarer medium. A convex spherical refracting surface with radius R separates a medium having a refractive index of 5/2 with respect to air.
• Concave Spherical Refracting Surface, which is concave towards the rarer medium.

Assumptions

When examining refraction at spherical surfaces, the following assumptions are taken into account:

(a) It is assumed that the incident light is monochromatic (single colour).

(b) The incident light beam is extremely close to the main axis (paraxial rays).

The sign conventions are the same as for spherical mirrors.

Key Terms Related to Refraction from a Spherical Surface

• Pole: The centre of the spherical refracting surface is called the pole of the surface.

• Centre of Curvature: The centre of the sphere of which the refracting surface forms a part is called the centre of curvature of the surface.
• The Radius of Curvature: The radius of the sphere of which the refracting surface forms a part is called the radius of curvature of the service
• Principal Axis: A hypothetical horizontal line drawn through the centre of the lens is the principal axis. The focal point of a perfect lens will be located on the principal axis at a range of the focal length from the lens’s centre.
• Aperture: The diameter of the periphery of the spherical refracting surface is called the aperture of the surface.

Coordinate Geometry Sign Convention for Measuring Distances and Lengths

To obtain common formulae for the positions and sizes of real and virtual images formed by convex and concave lenses, we have to adopt common conventions for given signs, either positive or negative, for the distances and lengths of the object and the images and the focal length of the lens. Different writers use different sign conventions, but most of them prefer the “Coordinate Geometry Sign Convention”. They are stated as below:

1. The light rays are always allowed to fall on the refracting surface or the lens from the left side.
2.  All distances are measured from the pole of the spherical surface or the optical centre of the lens, along the principal axis.
3. The distance measured in the direction of the incident light is taken with a positive sign, while those measured in the direction opposite to the direction of the incident light are taken with a negative sign.

According to this convention, the radius of curvature of a convex surface and the focal length of a convex lens is positive, while those of a concave surface and a concave lens are negative.

Law of Refraction

(a) The incident, refracted, and normal rays all lie in the same plane.

(b) For the two media through which light travels, the sine of both angles, that is, the angle of refraction to the angle of incidence, is constant.

Refractive Index=sin i sin r = Constant

The speed of light in the first medium through which the light travels to the speed of light in the second medium through which the light is refracted is also known as the refractive index of a medium.

Conclusion

A lens is a clear thick glass that is limited on two sides by spherical surfaces. It is an optical device that allows light beams to diverge or converge before being transmitted. Concave or divergent lenses and convex or convergent lenses are the two major types of spherical lenses. The focal point is where these rays converge or seem to diverge. The phenomenon of light refraction occurs when light travels from one medium to another. This path alteration occurs at the intersection of two media. When light travels from one medium to another, its speed changes, causing refraction. The phenomenon of refraction explains why lenses can converge or diverge light rays travelling through them. Many phenomena that are caused by refraction can be seen if we glance around.