Refraction at a spherical surface

Every day we come across plenty of spherical lenses unknowingly. But, we hardly realise how amazingly it works. For example, the spectacles you are wearing, the vehicle mirror you have, everything comes with a spherical surface. Little do we know about the refraction at a spherical surface.

A change in the light direction or just a bending in the light wave moving from transparent mediums is caused due to wave speed. This phenomenon is known as refraction. You will come across this phenomenon in nature. Lenses tend to converge or diverge light rays passing through it only due to refraction. Let us check out more about refraction.

Refraction through a spherical surface

Spherical surfaces are an integral part of the sphere. If you want to know about a common spherical surface, you will notice the spherical mirrors, a great example. Convex and concave are two common spherical surfaces. Convex is a surface that has curved outwards. A convex lens supports refraction from rarer to denser medium at a convex spherical refracting surface.

However, every concave lens comes curved inwards when it comes to the concave surface.

What are the derivations for the refraction of spherical surfaces for the pointed objects?

It is important to understand that the refraction at a spherical surface mainly occurs in two ways. A ray of light travels from the rare medium to dense medium, where the light bends towards the normal. Alternatively, the ray of light travels from the denser to the rarer medium, where the ray of light tends to bend away from the normal. Here are some of the considerations that you need to keep in mind.

• The object you are considering is point sized and is kept on the principal axis of the spherical refracting surface.
• The aperture of the refracting surface is small.
• Incident and the refracting rays make small angles with the principal axis of the spherical surface.

Two cases happen while considering the refraction at the spherical surface: refraction from denser to rarer medium at a convex spherical surface and a concave spherical surface. When considering refraction from dense to rare medium, two things occur—refraction from the dense to rare medium at the convex spherical surface and a concave spherical surface. 

Principal Axis and Optical Centre of a Lens

The central point of the lens is named the lens’s optical centre. The line that passes by the optical centre of the lens is commonly known as the principal axis. This phenomenon is known as the refraction at the spherical surface. Principal axis is perpendicular to the convex and concave surface of the lens.

Convex Lens – Principal focus & Focal Length – A parallel beam of light that travels by the principal axis and passes by the convex surface converges to a point on the principal axis. This point of refraction at a spherical surface is known as the principal focus. As the lens has two convex surfaces, the lens has two foci. 

Concave Lens – Principal focus and focal length – Principal focus is the point on the principal axis from where the light travels parallel to the principal axis, appearing to diverge after it passes through the concave lens. While focal length is the distance between optical centre & principal focus. 

Image formation by a lens

For determining position, an image is formed due to the spherical lenses; it is important to know the basic rules of image formation. Some of the basic and essential rules are discussed below. 

• Light travelling parallel with the principal axis from any object after passing from the convex lens gets refracted from the converges on the principal focus situated on the other side of the spherical lens. The ray of light passing through the lens diverges from the principal focus when it comes to the concave lens.
• In convex lenses, when travelling through the principal focus, a ray of light tends to travel parallel to the principal axis. When it comes to the concave lens, the light rays from the object tend to meet in the principal focus of the lens. This is a significant phenomenon of refraction at concave spherical surface derivation. Later on, it travels parallel to the principal axis. 
• When the light ray from the object travels from the optical centre in a concave and convex lens, it will travel straight without deviating. Image formation by a lens is a crucial part of the refraction at a spherical surface when it comes to image formation.

Convex lens – Image formation

Here, we will learn that the image is formed when light passes through the convex lens if an image is placed in front of the lens at five different positions. 

1. When any object is placed between the focus and the optical centre, the refraction of light at spherical surfaces lenses leads to the image formation behind the object, which is virtual, erect, and bigger than the object. Hence, it is clear that the convex lens can be used to magnify. . 
2. When the object is kept at the focus of the convex lens, images are formed at infinity. The refraction at a spherical surface creates real and inverted images. 
3. When the object is placed between F and 2F on the left of the lens, the image formed crosses the 2F on the right side of the lens. This results in a real and inverted image that looks bigger than the object. 

1. When the object is kept at 2F, the image formed due to the refraction from rarer to denser medium at a convex spherical refracting surface, the image formed is at the 2F distance on the right of the lens. It looks inverted, and the size is similar to that of the object.

1. When the object is kept beyond 2F on the left side of the lens, the image is formed within a distance of F and 2F on the right side of the lens, which results in inverted image formation than the object.

Conclusion

The refraction of light at spherical surfaces lenses is quite interesting and easy to understand since the same concept is applied everywhere in daily life. Whether it is a mirror or the spectacles you wear, these work on the simple phenomenon of refraction on the spherical surface; if you want to understand the entire concept of refraction at a spherical lens, then this information will help you. It will help you in understanding how the light rays behave when it enters a spherical lens. When combining the relations of refraction at a spherical surface of both the lenses, you will get the formula of the lens as the whole entity.