Critical Angle

Introduction

• When light travels from one medium to another, it changes its speed because the speed of light is determined by the medium it's passing through.

Speeding Up and Changing Angles

• When light speeds up as it moves from one material to another, the angle at which it refracts (bends) becomes larger than the angle of incidence (the angle at which it initially strikes the boundary).
• This phenomenon occurs, for example, when light travels from water to air or from glass to water.

Understanding Angles

• To understand critical angles, we need to consider the angles of incidence and refraction.
  • Angle of incidence: The angle between an incident ray (incoming light) and the normal (a line perpendicular to the surface).
  • Angle of refraction: The angle between a refracted ray (light inside the second medium) and the normal.

Critical Angle Defined

• The critical angle (denoted as θc) is a specific angle of incidence.
• When the angle of refraction equals 90 degrees (a right angle), the corresponding angle of incidence is called the critical angle.

Total Internal Reflection

• Beyond the critical angle, something interesting happens. Light is no longer refracted; instead, it is reflected entirely at the boundary.
• This phenomenon is known as total internal reflection.
  • "Total" because all the light energy is reflected.
  • "Internal" because the energy remains inside the material.
  • "Reflection" because the light is reflected back.

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Critical Angle

Practical Example

• As the angle of incidence increases beyond the critical angle, the angle of refraction gets closer to 90 degrees.
• Eventually, at an angle of incidence greater than the critical angle, all the light is reflected, and none of it passes through the surface.
• This total internal reflection is employed in optical fibres and prisms for various applications.

Relationship Between Critical Angle and Refractive Index

• The critical angle (θc) is related to the refractive index (n) of the material through the formula:
• n = 1 / sin(θc)
• This relationship allows us to calculate the refractive index of a material when the critical angle is known.