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Working with Light 187

traveling parallel to the principal axis on the way to a convex mirror will reflect in a manner that its
extension will pass through the focal point. Any incident ray traveling towards a convex mirror such
that its extension passes through the focal point will reflect and travel parallel to the principal axis.

REFRACTION:SNELL’S LAW
Refraction results when light is scattered in the same direction as that of incident light but passing
between dissimilar materials, the rays bend and change velocity slightly. Refraction is dependent
on two factors: the incident angle u, that is, the angle between the incident light and the normal to
the surface, and the refractive index, n of the material, defined as the ratio between the velocity of
the wave in vacuum (c v ) and the velocity of the wave in the medium (c s ),

c v
n ¼ : (5:2)
c s
The refraction results in the following relationship

sin (u 1 )
1 n 2 ¼ (5:3)
sin (u 2 )
where 1 n 2 is the refracting index in passing from Medium 1 to Medium 2 and u 1 and u 2 are the
angles made between the direction of the propagated waves and the normal to the surface separating
the two media.
For a typical air–water boundary, (n air ¼ 1, n water ¼ 1.333), a light ray entering the water at
458 from normal travels through the water at 32,118 (Figure 5.7).
The index of refraction decreases with increasing the wavelength. This angular dispersion
causes blue light to refract more than red, causing rainbows and prisms to separate the spectrum
(dispersion). Table 5.2 shows the refraction index of some common materials.

DISPERSION

Dispersion is a phenomenon that causes the separation of a light into components with different
wavelenghts, due to their different velocities in a medium other than vacuum. As a consequence,
the white light traveling through a triangular prism is separated into its color components, the spec-
trum of light. The red portion of the spectrum deviates less than the violet from the direction of
propagation of the white light (Figure 5.8).

FIGURE 5.7 Refraction of a light ray passing from a medium with lower refraction index (air) to a medium
with higher refraction index (water). u 1 , angle of incidence and u 2 , angle of refraction.