# Refractive index and critical angle relationship in circles

### Waves Tutorial 6

If the angle of incidence is bigger than this critical angle, the refracted ray will not light is travelling from an optically denser medium (higher refractive index) to. refractive index into a medium with a different refractive index. . Substituting s' from the general object-image relation, we get a more useful expression: . measured along a vertical circle, and a given azimuthal angle, .. incidence angle known as the critical angle, all light is reflected and Rs = Rp = 1, as. When light passes from a medium with one index of refraction (m1) to another At one particular angle (critical angle), the refracted light will not go into m2, but.

Mathematically, this would involve finding the inverse-sine of a number greater than 1. Physically, this would involve finding the critical angle for a situation in which the light is traveling from the less dense medium into the more dense medium - which again, is not possible. This equation for the critical angle can be used to predict the critical angle for any boundary, provided that the indices of refraction of the two materials on each side of the boundary are known.

Examples of its use are shown below: Example A Calculate the critical angle for the crown glass-air boundary. Refer to the table of indices of refraction if necessary. The solution to the problem involves the use of the above equation for the critical angle. Of all the possible combinations of materials that could interface to form a boundary, the combination of diamond and air provides one of the largest differences in the index of refraction values.

## Total internal reflection

This peculiarity about the diamond-air boundary plays an important role in the brilliance of a diamond gemstone. Having a small critical angle, light has the tendency to become "trapped" inside of a diamond once it enters.

A light ray will typically undergo TIR several times before finally refracting out of the diamond. Because the diamond-air boundary has such a small critical angle due to diamond's large index of refractionmost rays approach the diamond at angles of incidence greater than the critical angle. This gives diamond a tendency to sparkle.

The effect can be enhanced by the cutting of a diamond gemstone with a strategically planned shape. The diagram below depicts the total internal reflection within a diamond gemstone with a strategic and a non-strategic cut.

### Triple Physics Topic 5

Use the Find the Critical Angle widget below to investigate the effect of the indices of refraction upon the critical angle.

Simply enter the index of refraction values; then click the Calculate button to view the result. Either type of quarter-wave retarder may be used, for instance, to transform linear polarization to circular polarization which Fresnel also discovered and vice versa. The polarization dependent phase shift is also the reason why TE and TM guided modes have different dispersion relations [ dubious — discuss ].

Applications[ edit ] Mirror like effect Total internal reflection is the operating principle of optical fibers [3]which are widely used in telecommunications. Refractometers often use the critical angle to determine the refractive index of a substance.

### Brilliance - The Gemology Project

Prisms in binoculars use total internal reflection, rather than reflective coatings, to fold optical paths and show erect images. Optical fingerprinting devices use frustrated total internal reflection in order to record an image of a person's fingerprint without the use of ink.

A total internal reflection fluorescence microscope uses the evanescent wave produced by TIR to excite fluorophores close to a surface.

This is useful for the study of surface properties of biological samples. Gonioscopy employs total internal reflection to view the anatomical angle formed between the eye's cornea and iris [6] [7]. X-ray mirrors often achieve high reflectivity through total external reflectionthe equivalent of total internal reflection for refractive indices below 1.

A gait analysis instrument, CatWalk XT, [8] uses frustrated total internal reflection in combination with a high speed camera to capture and analyze footprints of laboratory rodents. By etching a grid pattern on the second surface of the LGP, frustrated total internal reflection occurs allowing the light to escape the LGP as visible illumination.

Brilliance is an overall visual perception based on the physical laws of refraction and reflection. When light hits the surface of a transparent optically denser medium like a gemstone it will be either reflected from the surface bounced back or partially refracted bent and sent in another direction inside the stone. When a light ray is refracted, it hits a pavilion facet and either is refracted out of the stone or reflected inside the stone depending on which angle the light ray approaches the facet Fig.

Every stone has an angle at which the light ray will either be refracted sent along a different path or reflected bounced back. This angle is known as the critical angle and depends on the refractive index of the stone how much the light ray is bent. The higher the refractive index, the smaller the critical angle. When a light ray approaches a pavilion facet at an angle larger than the critical angle, it will be completely reflected inside the stone.