Lecture 19- chromatic aberrations in simple lenses and the eye.pdf

Question 1

What does the longitudinal chromatic aberration show in the diagram? (first slide)

Answer 1

• the focal length of this thin lens varies with wavelength
• so if the image plane (which could be the same as the focal plane due to the distant object point ) is indicated, then the blue image plane will be much closer towards the lens
• the change in the focal length is caused by the change in the power of the lens which also causes a change of transverse magnificattion.
• If you have an extended object point, the image of this extended (distant object) of white light will consist of a series of images in different wavelengths because the power of the lens is different in different wavelengths and the magnification of image will be different which will cause colour fringes.

Question 2

What happens if you have a distant object?

Answer 2

-If you have an extended object point, the image of this extended (distant object) of white light will consist of a series of images in different wavelengths because the power of the lens is different in different wavelengths and the magnification of image will be different which will cause colour fringes.

Question 3

What happens in the human eye?

Answer 3

• also have chromatic aberration
• if the refractive state of the eye is such that the long wavelength of light is imaged on the retina, then the short-wavelength light will be imaged in front of the retina
• However, there is only one image plane - which is the retina- so blur rays will spread over red - so blue fringes - this becomes much larger when dealing with extended objects

Question 4

What are the limits of wavelength for human vision?

Answer 4

380 and 780nm

Question 5

What does the eye do?

Answer 5

the eye evolves to minimise the effect of chromatic aberration

Question 6

What does the eye do?

Answer 6

the eye evolves to minimise the effect of chromatic aberration

Question 7

Power of thin lens?

Answer 7

F = (nd - 1 )( c1 - c2 )

Question 8

How to determine changes in the power of light/wavelength:?

Answer 8

SUBTRACT THEM
SF = Fd / V
V= constrigence
-the change in lens power is due to dispersion.

Question 9

What is the V value?

Answer 9

• the constringence
• the reciprocal dispersive
  power
• the V-value of a dispersive
  material or the Abbe number!

Question 10

Why is the V value important?

Answer 10

The parameter, V, is important since it determines the difference in the power of

Question 11

How do we measure chromatic aberration in a simple lens?

Answer 11

EXAMPLE using yellow light
- yellow wavelength of light - as you move the object along the optical axis when the object hits the focal plane for a yellow light, then the light is imaged at infinity and is fully collimated
-the distance between the lens and the object is focal.
-Now if you replace with blue light - then the greater lens power(greater power for blue light )- the image will be at a finite distance because the beam of light will converge. to keep the light collimated and image at infinity we have to move an object towards lens through a small distance which you label little x. Little x is positive.
The focal length of blue light is negative and so is for yellow light

Question 12

How do you relate the change in lens power to the distance little x?

Answer 12

Fx = -1/ fd
-Take difference in powers between blue and yellow light
SF= Fd ( x/ f’d - x )

Question 13

Now, what about the human eye?

Answer 13

• we measure chromatic aberration in human eye via a achromatic doublet lens - it is possible to combine lenses with opposite powers - to ensure no chromatic aberration- lens will have the same power for all wavelengths
• If you place an object in focal plane of this achromatised lens you will eliminate the object with white light
• then all rays come out parallel to the axis in every wavelength and they will be sent to infinity- image is at infinity- the light is collimated in respect to the axis.

Question 14

What happens if you place eye here (where wavelengths of light are parallel) ? look at diagram 4th slide

Answer 14

• when this light enters the human eye, different wavelengths will be imaged at different distances due to chromatic aberrations in the eye -
• usually, the long-wavelength light is furthest away from the lens and the shorter near the lens

Question 15

What does this mean ?

Answer 15

this means that the power of the optics of the eye vary with wavelength

Question 16

What happens if you want to put a certain wavelength (such as blue in this diagram) onto the retina?

Answer 16

if we want to push the image plane onto retina you have to move an object towards lens until the divergence of the beam is now that by the increased power of blue light - so the blue image plane is now onto the retina.
-now have to find the change in power in the human eye for blue light.

Question 17

How do we find the change in power of the blue light in the human eye?

Answer 17

-see the change in power as a function of the distance little x
-the virtual image produced by this object in this achromatised lens becomes the position of the virtual object for the human eye when blue light is in focus
-equation F o = (x /
f ‘o - x )

Question 18

How do we deal with the effects of chromatic aberration?

Answer 18

• if we carry out exact ray tracing through a simple thin lens- the image planes shift horizontally along axis
• if you magnify the image you can see what wavelength is further away
• it is possible to combine 2 lenses - 1 of positive and 1 of negative power = the power will still be positive when added = F = F1 +F2

Question 19

Why can we choose a glass material?

Answer 19

ensure the change in power of the first lens is just Fd/ V and Fd2 / V2
-to ensure when adding these changes in power the answer comes as 0 - no change in power of the combination of the achromatised lens as light changes from blue to red - image hence sharply in focus- same image plane of both lights

Question 20

Achromatic combination of separated thin lenses in air

Answer 20

: d= (f1+f2)/2
When d equals (f1’+f2’)/2, the power of the combination becomes independent of wavelength. See Appendix!
-This means that the linear magnification is constant, hence no transverse chromatic aberration!
-meaning the focal length of blue light will equal that for red light

Question 21

Achromatic combination of thin lenses in air equation ?

Answer 21

: d= (f1+f2)/2

Question 22

What happens to the longitudinal chromatic aberration in this lens ?

Answer 22

• The image plane producing red and blue light are not at the same location along the axis in the diagram (of the achromatic combination of separated thin lenses)

Question 23

How does this come about ? ^

Answer 23

• can use the diagram to appreciate what happens
• the way we owkr the principle planes of the equivalent lens is to take rays which is parallel to axis and refract ray through first lens and 2nd lens then extended the direction of the final and incident tray and where these rays meet we have the principle plane of the equivalent lens. Fe - focal plane

Question 24

What happens as principle planes shift along axis ?

Answer 24

• As principle planes shift along axis, the focal planes also shift along axis

Question 25

What does change in image plane position represent ?

Answer 25

represents longitudinal chromatic aberration

Question 26

What is the conclusion of the use of the achromatism doublet lens?

Answer 26

-Although the lens is achromatised for every wavelength and the power of lens remains unchanged- the longitudinal chromatic aberration is not eliminated although the magnification of the image remains unchanged in any of the image planes

Question 27

A thin lens made from crown glass is free from chromatic aberration

Answer 27

z

Question 28

Glass of low V-value yields smaller chromatic aberration

Answer 28

z

Question 29

An achromatised doublet lens is completely free from chromatic aberration

Answer 29

z

Question 30

An achromatised doublet lens has equal power for red (nC) and blue (nF) light

Answer 30

z

Question 31

Two thin lenses made from the same glass material and separated by half the sum of their focal lengths

Answer 31

z