Figure 1-16 The fisherman must throw the spear in front of the virtual fish to hit the actual fish. (Illustration
developed b y Kevin M. Miller, MD, rendered b y Jonathan Clark, and modified b y Neal H. Ateb ara, MD.)
From your knowledge of Snell’s law, you know that the fish is not where it appears to be. If you throw the spear at the fish, you will certainly miss it. What you have to do is throw the spear in front of the virtual fish, the one you see, to hit the real fish.
Normal Incidence
Normal incidence occurs when a light ray is perpendicular to the optical interface. In other words, the surface normal coincides with the ray. If the interface is a refracting surface, the ray is undeviated. Light changes speed as it crosses the interface but does not change direction. If the surface reflects specularly, rays and pencils of light will be reflected back along a 90° angle to the surface.
Total Internal Reflection
Total internal reflection (TIR) occurs when light travels from a high-index medium to a low-index medium and the angle of incidence exceeds a certain critical angle. Under these circumstances, the
incident ray does not pass through the interface; all light is reflected back into the high-index medium. The law of reflection governs the direction of the reflected ray.
Figure 1-17A shows a light ray traveling from a high-index medium (spectacle crown glass) into a low-index medium (air). In this situation, the transmitted ray bends away from the surface normal, and thus the angle of transmission exceeds the angle of incidence. As the angle of incidence increases, the angle of transmission increases to a greater degree. Eventually, the angle of transmission equals 90°. At this point, the ray grazes along the optical interface and is no longer transmitted (Fig 1-17B).
Figure 1-17 A, When light travels from a high-index medium to a low-index medium, it bends away from the surface normal. B, At the critical angle, θc, the refracted light travels in the optical interface. C, Beyond the critical angle, all light is reflected by the interface. In A and B, light is also reflected by the interface (not shown). (Illustration developed b y Kevin M. Miller,
MD, and rendered b y C. H. Wooley.)
The critical angle is the angle of incidence that produces a transmitted ray 90° to the surface normal. The critical angle, θc, is calculated from Snell’s law:
ni sin θc = nt sin 90°
The sine of 90° is 1; thus, ni sin θc = nt
Rearranging gives
So, the angle of transmission is 90° when the angle of incidence is
In the current example, ni = 1.000 and nt = 1.523, so the critical angle is 41.0°.
What happens when the angle of incidence exceeds the critical angle? As Figure 1-17C shows, the angle of transmission increases as the angle of incidence increases, but the angle of transmission cannot exceed 90°. Consequently, refraction cannot occur. Indeed, Snell’s law has no valid mathematical solution (in real numbers) when the critical angle is exceeded. Instead, the incident ray is 100% reflected.
TIR is a rather curious phenomenon. Consider light traveling from spectacle crown glass to air. If the angle of incidence is 10°, the light transmits easily as it crosses the interface. However, if the angle of refraction is 45°, the interface becomes an impenetrable barrier! The interface is transparent to some rays and opaque to others. Physicists have devoted considerable attention to this phenomenon.
TIR has great practical value. In the early 1600s, it was difficult to make a good mirror. The best surfaces could specularly reflect only about 80% of incident light, and the rest was diffusely reflected, which made these surfaces nearly useless as imaging devices. However, TIR is just that— total. When TIR occurs, 100% of the light is reflected. In the past, often the only way to make a practical mirror was to use internally reflecting prisms. Today, TIR is still used in prisms within binoculars, slit lamps, and operating microscopes, for example. Clinically, TIR is a nuisance when clinicians are trying to examine the anterior chamber angle. (See Clinical Example 1-5.)
Clinical Example 1-5
Total internal reflection (TIR) makes it impossible to view the eye’s anterior chamber angle without the use of a contact lens. Light from the angle undergoes TIR at the air–cornea interface (technically, the air–tear-film interface) (Fig 1-18A). Light from the angle never escapes the eye. Using a contact lens to eliminate the air at the surface of the cornea (Fig 1- 18B) overcomes the problem. Light travels from the cornea (or coupling gel) to the higher- index contact lens. TIR never occurs when light travels from a medium of lower index to one of higher index, so light enters the contact lens and is reflected from the mirror. TIR does not occur at the front surface of the contact lens because the angle of incidence is less than the critical angle.
Figure 1-18 A, Light from the anterior chamber angle undergoes total internal reflection (TIR) at the air–tear- film interface. B, A contact lens prevents TIR and allows visualization of the angle structures. (Illustration
developed b y Kevin M. Miller, MD, and rendered b y C.H. Wooley.)
Assuming the refractive index of the tear film on the front surface of the cornea is 1.333, the critical angle for the air–tear-film interface is