Imaging with a thick lens Flashcards
why use cardinal points?
the basic imaging properties such as image size, location, and orientation are completely determined by the locations of the cardinal points
Where do we act like all the refractions occur at in thick lens?
principal planes
nodal points
have the property that a ray aimed at one of them will be refracted by the lens such that it appears to have come from the other. and with the same angle with respect to the optical axis
Assumptions of thin lenses
- both sides in same medium
- lens is thin, 0 thickness
- paraxial approximation
how can you tell in a thin lens, that the same medium is on both sides of the lens
equal focal lengths on either side of the lens
if the focal length is shorter on one side of the thin lens…
the short side is in a medium with higher RI
principle plane
- refraction happens at principle plane
- not really a flat surfaces
- curved
principal point
where the principle plane intersects the optical axis
Rule number 1 in thick lens
parallel then refracts at H’
rule number 3 of thick lens
goes towards N, goes straight across to N’ and then comes out of lens at the same angle as it entered lens
ANGLE PRESERVATION
there is a virtual parallel displacement from N’ to N
P=N
in a lot of thick lens systems, but not always
actual rays
are subjected to two refractions, one per refracting surface
conventional rays
change path only when encounter the prinicple planes (parallel and focal ray) or the nodal points (the nodal/radial ray)
Ray propagation in a thick lens
rays do not pass through the cardinal points, however it is very useful to follow the rules of conventional rays to find the final path of any ray
object distance in thick lens
measured from H
image distance in thick lens
measured from H
thick lens imaging relationship
1/xo + 1/Feff = 1/xi
focal length measurement when rays propagating from right to left
measured from the principal plane H’
focal length measurement when rays are propagating from left to right
measured from the principal plane H
thin lens in contact optical power
Ptot=P1+P2
optical power in a lens system: general
Ptot=P1+P2-(d/n)P1P2
optical power in lenses separated by distance in air
Ptot=P1+P2-dP1P2
d
the distance from the object space principal plane of the first lens (H’) to the image space principal plane (H’2) of second lens
for calculation of the principle point locations as well as nodal point locations
use the object space principal plane of the first lens (H1), and for the image space, the image space principal plane (H’2) of the second lens
the origin from which we measure gamma and gamma’ as well as thickness (d)
principal point P1 and the principal point P2 respectively.
these points now have the role of the respective V and V’ points
imaging with two or more lenses
- we find the reduced system cardinal points
- locate the image by application of the thick ray diagrams
OR
employ the analytical expressions
use of the intermediate object
- find the location and size of the primary image by applying summation of beam vergence and optical power (analytical solutions)
OR
locate the primary image with ray fiagrams apllicable for a single, thin lens (schematic solution) - this is the intermediate object. The pricedure may be repeated for any additional optical element
Use of intermediate object
- if 2nd lens appears to block the construction rays, we ignore it for now
- to find final image from intermediate object, we now ignore first lens and trace rays and find image location as normal
