Читать книгу Optical Engineering Science - Stephen Rolt - Страница 23

Thus far, we have presented a description of an idealised optical system. Is there a simple condition that needs to be fulfilled in order to generate such an ideal image? It is easy to see from Figure 1.11 that the following relations apply:

Therefore:

As we will be able to show later, the ratio f₂/f₁ is equal to the ratio of the refractive indices, n₂/n₁, in the two media (object and image space). Therefore it is possible to cast the above equation in its more usual form, the Helmholtz equation:

(1.8)

One important consequence of the Helmholtz equation is that there is a clear, inextricable linkage between transverse and angular magnification. Angular magnification is inversely proportional to transverse magnification. For small θ, tan θ and θ are approximately equal. So in the small signal approximation, the angular magnification, α is given by:

Hence:

(1.9)

We have, thus far, introduced two different types of optical magnification – transverse and angular. There is a third type of magnification that we need to consider, longitudinal magnification. Longitudinal magnitude, L, is defined as the shift in the axial image position for a unit shift in the object position, i.e.:

(1.10)

From Newton's Eq. (1.6):

And:

(1.11)

Thus, the longitudinal magnification is proportional to the square of the transverse magnification.