Simple Lens Systems

Abstract

The change in curvature of a wave front by a lens can be considered in two stages: first the change as the wave front enters the lens and then the change as it leaves. Consider now the passage of a wave front from a medium of index µ _p , where its radius of curvature is p, into a medium of index µ _q , the boundary surface itself having radius of curvature r (Figure 29.01). Let the equations of the incident wave front and of the lens be

$${x_p} - {x_{0p}} = \frac{{{y^2}}}{2}\frac{1}{p}$$

and

$${x_r} - {x_{0r}} = \frac{{{y^2}}}{2}\frac{1}{r}$$

Then by allowing a time ∆t sufficient for the wave front to enter the second medium, it may be shown much as in section 28.08 that the equation of the wave front in the q medium is

$$\frac{{{\mu _q}}}{q} = \frac{{{\mu _p}}}{p} + \frac{{{\mu _q} - {\mu _p}}}{r}$$

((29.01))

If the curvature of the boundary surface is zero, this reduces to

$$\frac{{{\mu _q}}}{q} = \frac{{{\mu _p}}}{p}$$