Refraction And Reflection of Plane Waves

Refraction is referred to as the bending of a light wave as it transitions from one medium to another. Like reflections, refraction occurs in different types of waves, such as sound waves or water waves. The index of refraction is the ratio of the light speed in a vacuum to the speed of light in a medium, µ = c / v. At the point of the incident, the light beam bends toward the normal when it travels from a rarer medium to a denser medium. In contrast, at the point of the incident, the light beam bends away from the normal when it travels from a denser medium to a rarer one.

Law Of Reflection

The forward propagation of light through scattering is impeded when it encounters a barrier (from one medium to another). Reflection occurs when the incident light is scattered backwards without cancellation.

According to the law of reflection,

• The incidence angle is the same as the reflection angle. θi = θr
• The plane of incidence is where the incident ray, the normal to the surface, and the reflected ray, all intersect.

The law of reflection describes the light waves’ behaviour as they hit a surface. Take a look at a mirror. Incident Ray is the light wave that travels towards the surface. The reflected ray is the light wave that rebounds back after contacting the surface.

Law Of Refraction

As soon as the beam enters the surface, lateral scattering becomes unimportant, and forward transmission takes over. The ray bends when the incident light is directed at an angle to the normal. Refraction is the term for this phenomenon. The bending is caused by the difference in speed when the beam moves from one medium to another and the fact that the beam’s width is limited.

Refraction

Refraction is the bending or changing of the direction of a light wave passing through a transparent medium induced by a change in the wave’s speed.

Refraction in Rarer Medium

The refractive index of the medium and the angle between the ray and the line perpendicular (normal) to the surface separating the two media determine how a wave bends.

Snell’s Law

Willebrord Snell, a Dutch physicist, discovered that the ratio of sines of the angle of incidence (i) and angle of refraction (r) is much like the proportion of velocities (v₁ / v₂) in the two mediums, or equivalently, the opposite ratio of indices of refraction.

(n₂ / n₁): n = sin i/sin r

Reflection of Plane Wave

The process through which a light wave strikes an item and bounces back is wave reflection. Not just light waves but also sound waves, infrared waves, and radio waves go through this process. When light strikes a smooth, clean surface, the light rays return at the same angles. This sort of reflection is called Specular Reflection. Specular reflection is the light that reflects from the surface of a mirror. When light rays strike an uneven surface, they bounce back at varied angles. Diffuse reflection is the term used for this phenomenon.

The behaviour of light waves as they impact a surface is described by the law of reflection. Incident Ray is the light wave that moves towards the surface. The reflected ray is the light wave that rebounds back after contacting the surface. Consider the spot on the surface where the ray is incident. Then draw a line that is perpendicular to the mirror’s surface. The sketched line is known as the Normal Line.

The angle formed by the incident and reflected rays is divided into two equal angles by the normal line. These two angles will be the incidence angle and the reflection angle. As a result, the angle of incidence equals the angle of reflection, according to the law of reflection. Also, the incident ray, reflected ray, and the normal drawn at the point of incidence are always in the same plane.

Reflection of a plane wave through the Huygens principle

Imagine the plane wavefront as AB that is incident on the surface. Let v1 and v2 be the incident and the refracted ray velocities of the medium 1 and 2, respectively (v₁ > v₂). The waves’ velocity is determined by the medium. The secondary spherical wavelet source comes from Huygens’ principles A and C. Imagine t as the time it takes to get from B to C.

As a result,

BC = v₁t in medium 1

Let’s draw the sphere of the radius v2t from point A, the second medium, to calculate the shape of the refracted wavefront. At time t, it represents the secondary spherical wavefront.

In medium 2,

AD = v₂t.

The tangent formed from point C to the sphere is now CD. The refracted wavefronts are thus AD and CD.

Take a look at ABC and ADC now.

(BC/AC) / (AD/AC) = Sin i / Sin r

BC/AD = v₁t/v₂t

= v₁/v₂

Refraction using the Huygens principle

When light passes through one transparent substance and then into another transparent material, its path changes. The angle of incidence is the angle between the incident ray and the normal, and the angle of refraction is the angle between the refracted ray and the normal, according to refraction rules.

The incident ray, reflected ray, and normal to any two mediums’ interface lie in the same plane. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is also known to be constant.

Conclusion

• As the light beam travels from a thin medium to a dense medium, it bends toward the normal at the point of incidence.
• The bending of waves when they pass through several mediums is known as refraction.
• The phenomenon of light waves colliding with the surface and bouncing back is known as reflection.
• Huygens’ Principle is used to verify the laws of reflection. The refracted ray, the normal ray, and the incident ray to the reflecting surface are all perpendicular and lie in the same plane. The angle of reflection is equal to the angle of incidence.