Reflection & Refraction – Curved Boundary

Yes! As light crosses the boundary from a faster medium to a slower medium it bends towards the normal.

Yes! When light leaves a vacuum or travels from one transparent medium into another, it undergoes refraction causing it to change both direction and speed.

Refraction refers to the way light changes both direction and speed as it travels from one transparent medium into another.

The normal is an imaginary line drawn on a ray-tracing diagram perpendicular to, so at a right angle (90 degrees), to the boundary between two media.

Refraction refers to the way light changes speed and direction as it travels across the interface between one transparent medium to another.

The angle of refraction measures the angle to which light bends as it passes across the boundary between different media.

• The angle of refraction is measured between a ray of light and an imaginary line called the normal.
• In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (90⁰), the boundary between two media.
• See this diagram for an explanation: Refraction of a ray of light
• If the boundary between the media is curved, the normal is drawn perpendicular to the boundary.

The refractive index (index of refraction) of a medium measures how much the speed of light is reduced when it passes through a medium compared to its speed in a vacuum.

• Refractive index (or, index of refraction) is a measurement of how much the speed of light is reduced when it passes through a medium compared to the speed of light in a vacuum.
• The concept of refractive index applies to the full electromagnetic spectrum, from gamma-rays to radio waves.
• The refractive index can vary with the wavelength of the light being refracted. This phenomenon is called dispersion, and it is what causes white light to split into its constituent colours when it passes through a prism.
• The refractive index of a material can be affected by various factors such as temperature, pressure, and density.

The angle of reflection measures the angle at which reflected light bounces off a surface.

• The angle of reflection is measured between a ray of light which has been reflected off a surface and an imaginary line called the normal.
• See this diagram for an explanation: Reflection of a ray of light
• In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (90⁰), the boundary between two media.
• If the boundary between the media is curved then the normal is drawn perpendicular to the boundary.

The refractive index (index of refraction) of a medium measures how much the speed of light is reduced when it passes through a medium compared to its speed in a vacuum.

• Refractive index (or, index of refraction) is a measurement of how much the speed of light is reduced when it passes through a medium compared to the speed of light in a vacuum.
• The concept of refractive index applies to the full electromagnetic spectrum, from gamma-rays to radio waves.
• The refractive index can vary with the wavelength of the light being refracted. This phenomenon is called dispersion, and it is what causes white light to split into its constituent colours when it passes through a prism.
• The refractive index of a material can be affected by various factors such as temperature, pressure, and density.

In physics and optics, a medium refers to any material through which light or other electromagnetic waves can travel. It’s essentially a substance that acts as a carrier for these waves.

• Light is a form of electromagnetic radiation, which travels in the form of waves. These waves consist of oscillating electric and magnetic fields.
• The properties of the medium, such as its density and composition, influence how light propagates through it.
• Different mediums can affect the speed, direction, and behaviour of light waves. For instance, light travels slower in water compared to a vacuum.
• Examples of Mediums:
  • Transparent: Materials like air, glass, and water allow most light to pass through, with minimal absorption or scattering. These are good examples of mediums for light propagation.
  • Translucent: Some materials, like frosted glass or thin paper, partially transmit light. They allow some light to pass through while diffusing or scattering the rest.
  • Opaque: Materials like wood or metal block light completely. They don’t allow any light to travel through them.

The angle of incidence measures the angle at which incoming light strikes a surface.

• The angle of incidence is measured between a ray of incoming light and an imaginary line called the normal.
• See this diagram for an explanation: Reflection of a ray of light
• In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (90⁰), the boundary between two media.
• If the boundary between the media is curved, then the normal is drawn at a tangent to the boundary.

Incident light refers to light that is travelling towards an object or medium.

• Incident light refers to light that is travelling towards an object or medium.
• Incident light may come from the Sun, an artificial source or may have already been reflected off another surface, such as a mirror.
• When incident light strikes a surface or object, it may be absorbed, reflected, refracted, transmitted or undergo any combination of these optical effects.
• Incident light is typically represented on a ray diagram as a straight line with an arrow to indicate its direction of propagation.

If one line is normal to another, then it is at right angles to it.

In geometry, normal (a or the normal) refers to a line drawn perpendicular to a given line, plane or surface.

• How the normal appears in a geometric drawing depends on the circumstances:
  • When light strikes a flat surface or plane, or the boundary between two surfaces, the normal is drawn perpendicular to the surface, forming a right angle (90°) with it.
  • Expressed more formally, in optics, the normal is a geometric construct, a line drawn perpendicular to the interface between two media at the point of contact. This conceptually defined reference line is crucial for characterizing various light-matter interactions, such as reflection, refraction, and absorption.
  • When dealing with curved surfaces, such as those found on spheres or other three-dimensional objects, determining the normal requires a slightly different approach. Instead of simply drawing a line perpendicular to the surface as with a flat plane, draw the normal straight up from the point where light hits the surface.
  • When considering a sphere, the normal line passes through the centre of the sphere. This is because, regardless of where light enters or exits the sphere, the normal represents the direction perpendicular to the surface at that point.

A tangent to a circle is a straight line that touches but does not intersect the circle and is at right angles to a radial line drawn from the centre of the circle.

• There are two main contexts to consider:
  • Circles: A tangent to a circle is a straight line that touches the circle at exactly one point – like a line just brushing against a ball. There’s also a special property – the radius drawn from the centre of the circle to the point of touch is always perpendicular (at a 90-degree angle) to the tangent line.
  • General Curves: A tangent line can also be applied to any smooth, curved shape. Here, the concept gets a bit more mathematical. We can define a tangent as a straight line that intersects the curve at exactly one point, but if we could zoom in infinitely close to that point, the curve would begin to resemble a straight line, and the tangent line would become indistinguishable from the curve itself.