ABSTRACT
Total internal reªection ªuorescence microscopy (TIRF) makes use of the quantum nature of light to form a ªuorescence image under conditions that are forbidden by conventional ray optics (Axelrod, 2001). The image comes from a very thin layer at the top surface of a sample and thereby offers resolution in the axial (Z) direction which confocal microscopy cannot match. To understand how TIRF works, we Žrst must understand total internal reªection, so here is a quick refresher. We have already encountered Snell’s law: sin i/sin r = n, where n is the refractive index, and i and r are the angles made to the normal by the incident and refracted rays. In this formulation, Snell’s law applies going from a medium of refractive index 1 (i.e., air or vacuum) into a medium of refractive index n. Because light ray paths are generally reversible, Snell’s law can be applied in reverse to deal with a ray passing from a denser medium (high n) into a less dense one. Of course, the less dense medium need not be air. It could be almost anything but for our purposes the most likely case is water (n = 1.3, or a bit more if anything is dissolved in it). So, it might be worth generalizing the formula as follows:
sinθ1/sinθ2 = n2/n1
where the sufŽxes 1 and 2 refer to the lower and higher refractive index media, respectively. Thus, going from air into glass n1 is 1, and the simple form of the equation applies. If we are going the other way, from glass into air, the exit angle will always be larger than the entry one, and eventually it will reach 90°, where the emerging ray travels parallel to the glass surface. Any higher value for θ2 would make θ1 larger than 90°, so the ray cannot exit from the glass. Instead, it is reªected, following the normal laws of reªection, and this is called total internal reªection. At what angle will this happen? If θ1 = 90°, then sin θ1 = 1, so this is pretty simple to work out. This value of θ2 is called the critical angle, θc, and is given by
sin θc = n1/n2
Going from glass into air, this works out to sin-1 (1/1.5), which is 42°. This calculation explains why we can use 90° prisms as perfect mirrors (for example, in a binocular head). In this case θ2 = 45°, which is greater than θc, so all the light is reªected.
