Refraction at spherical surfaces

Introduction

The bending of light beams at the meeting point of two transparent media is known as refraction. This is due to a shift in the direction of the light wave as well as the bending of light waves at the media’s meeting point. Refraction  through a spherical surface happens when the speed of a light wave changes when it approaches a new spherical surface, resulting in a change in direction or bending of the light wave.

Laws Of Refraction 

There are two laws of refraction. 

1. All the three rays – incident ray, normal and refracted ray lie in the same plane. 
2. The ratio of the sine angle of incidence to the sine angle of refraction is always constant, for a given pair of mediums. This law is also known as snell’s law and this constant is known as the refractive index. 

Refraction at spherical surface formula

 Refraction at spherical surface formula is also known as snell’s law

n1sin𝞱1 = n2 sin𝞱2

n1 = refractive index of medium 1

𝞱1 = incident angle

n2  = refractive index of medium 2

𝞱2 = refracted angle

Refractive Index

The refractive index is a metric that measures how far light rays bend when they enter another medium. The letter ‘n’ stands for refractive index.

‘n’ is a derived variable.

It’s the ratio of c and  v.

Where c is the velocity/speed of light in the air of a specific wavelength, and v denotes the speed of light in any medium.

Refraction At Spherical Surfaces 

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.

When two spherical lenses come in contact with each other (face to face), it forms a shape of a spherical lens. Spherical lenses are of two types – concave lens and convex lens. When the ray of light passes through the concave lens, it forms a virtual, erect and diminished image. 

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. 

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 

This article explains refraction at spherical surfaces. The bending of light beams at the meeting point of two transparent media is known as refraction. Refraction at spherical surface formula is also known as snell’s law and according to this law, the ratio of the sine angle of incidence to the sine angle of refraction is always constant, for a given pair of mediums.