Editorial Feature

# ant Critical Angle - Definition and Applications

Critical angle in optics refers to the angle of incidence, beyond which total internal reflection of light occurs. The path of a light ray incident upon a medium that has a lesser value of refractive index is bent away from the normal path. As a result, the exit angle of the ray is greater than the incident angle. This reflection is termed as internal reflection.

Whenever light travels from a medium of higher refractive index (n1) into a medium of lower refractive index (n2), like from glass to air, the angle of refraction is greater than the angle of incidence.

As a result of the difference in refractive index, the ray will be bent towards the surface. As the incident angle is increased, the angle of refraction will approach 90°. When the angle of refraction reaches 90° there is no light transmitted into air. This angle of incidence is called the critical angle.

## Calculation of Critical Angle

Snell’s law is used to calculate the values of critical angle. According to Snell’s law, the ratio of the sines of the angle of incidence and refraction is equivalent to the ratio of the phase velocities of the two media.

Consider two media with refractive indices of n1 and n2 (n2>n2) and angle of incidence θ1, angle of refraction θ2, and critical angle θc. The value of sin θ2 is equal to 1, as value of θ2 is equal to 90°. Re-arranging Snell’s law equation, we get the equation for critical angle as:

θ1 = θ1=arc sin(n1/n2)

## Applications of Critical Angle

The concept of critical angle is the basis for the construction and working of fiber optic cables. Some of the typical applications of total internal reflection are listed below:

• Optical fiber communication
• Automotive rain sensors
• Spatial filtering of light
• Working of total internal reflection fluorescence microscope
• Multi touch screens
• Prismatic binoculars