Refraction at plane and spherical surfaces

Introduction

The velocity of light in vacuum is 3×10⁸ m/s. It travels in a straight line. When light passes through a material, the speed of light alters. The properties of the path of light involve three different principles – reflection, diffraction, and refraction. These properties are essentially included when designing or constructing commercial products and instruments. The light refraction at the plane and spherical surfaces differs widely.

Path of light 

Light rays tend to travel in a straight line. But when there is an obstruction, the path of light changes. Sometimes, the direction and speed change too. Such change in the path of travel is common in any electromagnetic wave.

Properties of Light

Reflection of light rays

• When the light hits a polished, opaque plane surface, the light rays change their direction to the opposite side of travel at a particular angle. 
• This angle is the angle of reflection. It is an angle formed between the Normal of the surface and the reflected ray. 
• In reflection, the angle of incidence is always equal to the angle reflection.

Diffraction of light rays

• Diffraction is a change in the path of light that occurs when the light faces an interference during travel.
• For example, when a beam of light passes through a small opening, the light rays shift the path to enter the other side of the opening. It is most likely a diffusion process.

Refraction of light rays

• Under certain conditions, these light rays bend at an angle along the same path. This occurs due to the refraction of light. 
• Refraction is the bending of light rays when it passes through a transparent material that differs in its optical density.
• The refraction at the plane and spherical surfaces is different because of the different possible normals of the surfaces.

Refraction at the plane and spherical surfaces

Refraction of light occurs when the light rays:

• Falls at an angle greater than zero with the normal
• From one medium to another that has different optical densities

Refraction of light causes the rays:

• To change its speed
• To change its path
• To reduce concentration, as some are reflected away.

Refractive index

Refractive index is the measure of the speed of light in a medium. It often differs with medium and is related to the optical density of the medium that the light passes through. 

Law of refraction 

According to the law of refraction, the refractive index of a medium is calculated through the formula:

n = c / v where,

‘n’ is the refractive index of a medium

‘c’ is the speed of light

‘v’ is the phase velocity of light in the medium

It is a unitless measurement. As both the values are in terms of speed (m/s), it cancels out each other.

Refraction at Plane Surfaces in Different Media

The axis of refraction is the same for a particular angle of incidence, irrespective of the point of incidence on a plane surface. This is because the surface is plain and free of any topographical deflection.

• Lighter to denser – the refracted ray inclines towards the normal of the plane surface, in the case when an oblique light ray travels from an optically rarer medium to a denser medium. Example – air to glass or water.
• Denser to lighter – the refracted ray moves away from the normal of the plane surface when an oblique light ray passes from an optically denser medium to a rarer medium. Example – glass to air or vacuum.
• Zero refraction – When light passes along the normal of the plane surface through a transparent medium, the refraction angle is zero even when the density of the media varies.

Examples 

• The pencil seems broken and deflected along another angle when it is half immersed in a glass of water.
• The floor of a water body seeming shallow from the land
• A 3D object appears as 2D when completely immersed inside water.

Refraction at spherical surfaces

• Refraction at spherical surfaces can be well demonstrated with different curved lenses.
• The axis of refraction changes on a curved surface along with the change in point of incidence.
• This is because even when the angle of incidence is the same, the normal of the surface changes at every point of incidence, as it is a curved surface. 

Refraction at the Double Convex Lens

• A double convex lens appears like two convex lenses stuck against each other at the planar side. It converges the incident light rays.
• The light rays converge at the convex surface(air to glass) like the convex lens.
• Then incidents on the second glass.
• As a concave surface, it converges the light further(glass to air)

Refraction at the Double Concave Lens

• A double concave lens appears like two concave lenses stuck against each other at the planar side. It diverges the incident light rays.
• The light rays diverge at the concave surface(air to glass) like the concave lens. 
• Then incidents on the second glass. 
• It diverges the light further(glass to air) as a convex surface.

Conclusion

The light refraction at the plane and spherical surfaces results from different optical densities of the medium that the rays pass through. Thus, refracted rays move toward the normal when passing from rarer to denser medium. When passing from a denser to a rarer medium, it moves away from the normal. It is common to both planar and spherical surfaces.