2. Today . . . Multiple Lenses The Eye Magnifiers & Microscopes
Corrective Lenses for Myopic & Hypertropic Eyes
Magnifiers & Microscopes
Telescopes
Text Reference: Chapter 34.2,4
Examples: 34.9,10,12,13,14 and 15

3. Multiple Lenses
Draw Rays !
We determine the effect of a system of lenses by considering the image of one lens to be the object for the next lens.
f = +1
f = -4 -1 +3 +1 +2 +6 +5 +4
For the first lens: s1 = +1.5, f1 = +1 \
For the second lens: s2 = +1, f2 = -4 \

4. Multiple Lenses
Objects of the second lens can be virtual. Let’s move the second lens closer to the first lens (in fact, to its focus):
f = +1
f = -4 -1 +3 +1 +2 +6 +5 +4
For the first lens: s1 = +1.5, f1 = +1 \
For the second lens: s2 = -2, f2 = -4 \
Note the negative object distance for the 2nd lens.

5. Lecture 27, ACT 1 (c) m’ > m (a) m’ < m (b) m’ = m (a) real
Suppose we interchange the converging and diverging lenses in the preceding case.
What is the relation of the new magnification m’ to the original magnification m? 1A
f = +1
f = -4 -1 +3 +1 +2 +6 +5 +4
(c) m’ > m
(a) m’ < m
(b) m’ = m
What is the nature of the final image? 1B
(a) real
(b) virtual

6. Lecture 27, ACT 1 (a) m’ < m (b) m’ = m (c) m’ > m
Suppose we interchange the converging and diverging lenses in the preceding case.
What is the relation of the new magnification m’ to the original magnification m? 1A
(a) m’ < m
(b) m’ = m
(c) m’ > m
f = -4
f = +1 -1 +1 +2 +3 +4 +5 +6
Since the formula for the magnification is equal to the product of the magnifications of each lens (m = m 1 m 2), you might think that interchanging the lenses does not change the overall magnification.
This argument misses the point that the magnification of a lens is not a property of the lens, but depends also on the object distance!
Consider the ray shown which illustrates that the magnification must be < 1!

7. Lecture 27, ACT 1 (a) m’ < m (b) m’ = m (c) m’ > m (a) real
Suppose we interchange the converging and diverging lenses in the preceding case.
What is the relation of the new magnification m’ to the original maginification m? 1A
(a) m’ < m
(b) m’ = m
(c) m’ > m
f = -4
f = +1 -1 +1 +2 +3 +4 +5 +6 1B
What is the nature of the final image?
(a) real
(b) virtual
The ray used in part A actually shows that the image is real and inverted.
The equations:

8. This is called “accommodation”
The Eye
The “Normal Eye”
Far Point º distance that relaxed eye can focus onto retina = ¥
Near Point º closest distance that can be focused on to the retina
= 25 cm
2.5cm
25cm
Therefore the normal eye acts as a lens with a focal length which can vary from 2.5 cm (the eye diameter) to 2.3 cm which allows objects from 25 cm ® ¥ to be focused on the retina!
This is called “accommodation”
Diopter: 1/f Eye = 40 diopters, accommodates by about 10%, or 4 diopters

9. An intuitive way to view eye corrections
Near-sighted eye is elongated, image of distant object forms in front of retina
Add diverging lens, image forms on retina
Far-sighted eye is short, image of close object forms behind retina
Add converging lens, image forms on retina

10. Does the orientation of the lens matter?
Not according to our simple lens equation
assumes paraxial rays
In reality…
Spherical
aberration
As a general rule, it is better to split the refraction at both interfaces.
www-optics.unine.ch/education/optics_tutorials/plano_convex_lens_aberration.html

11. Why use two lenses instead of one?
No choice vision correction
Improve aberrations
Spherical Aberration
Chromatic Aberration
www-optics.unine.ch/education/optics_tutorials/achromat.html

12. Special Lens Combinations
If two thin lenses are close together, they act effectively as a single lens. The focal length of the “doublet” is given by f1 f2 {
fdoublet
Note the power (=1/f) of the combination is just Pdoublet = P1 + P2

13. Lecture 27, ACT 2
Hildegard’s retina is 2.5 cm behind the lens, which has a minimum focal length of 2.6 cm.
1. What does the focal length fcl of her contact lens need to be?
2.5 cm
feye = 2.6 cm
(a) 65 cm
(b) -65 cm
(c) -0.1 cm
2. What is the power Pcl of the contact lens?
(a) 1.5 D
(b) D
(c) 1000 D

14. Lecture 27, ACT 2
Hildegard’s retina is 2.5 cm behind the lens, which has a minimum focal length of 2.6 cm.
1. What does the focal length fcl of her contact lens need to be?
2.5 cm
feye = 2.6 cm
(a) 65 cm
(b) -65 cm
(c) -0.1 cm

15. Lecture 27, ACT 2
Hildegard’s retina is 2.5 cm behind the lens, which has a minimum focal length of 2.6 cm.
2.5 cm
feye = 2.6 cm
2. What is the power Pcl of the contact lens?
(a) D
(b) 1.5 D
(c) 1000 D
Note: We could have solved for the power directly:

16. Apparent Magnification
Our sense of the size of an object is determined by the size of image on the retina.
Consequently, the apparent magnification factor of a lens is just the ratio of the angular size with the lens to the angular size without the lens.
Use lens to make close up image fall in focus range of eye
Positive “f” lens a
Lnp h
Object at Near Point - can’t get nearer ~f b h
Object just inside Focal Point
of simple magnifier
Define Angular Magnification:

17. Microscope
Larger magnifications than are possible with a single lens can be obtained by combining lenses.
For example, the compound microscope consists of two lenses, a short focal length objective lens and an eyepiece:
The object, placed just beyond the focal point of the objective, produces a real, inverted image (I1) at a position which is just inside the focal length of the eyepiece. I2
~fo
~fe
eyepiece
objective L I1
This image then produces a virtual image (I2) which is seen as magnified as in the previous slide.
The magnification of the objective is:
The magnification of the eyepiece is:
The total magnification M = MoMe is:

18. Telescopes
The purpose of a telescope is to gather light from distant objects and produce a magnified image.
Refracting telescopes use lenses so that the objects can be viewed directly.
As in the microscope, we have two lenses, an objective and an eyepiece.
Since the object is at a large distance, the objective lens should have a long focal length to obtain a large magnification.
Reflecting telescopes use mirrors to create the image
Most astronomical telescopes are reflectors, since the most important feature for these telescopes is the light gathering ability, and it is easier to make a large mirror than it is to make large lenses.
detector

19. Hubble Space Telescope
The HST was launched in 1990; it was discovered that a lens had been ground incorrectly, so all images were blurry!
A replacement “contact lens”, COSTAR, was installed in 1993.
Before COSTAR
After COSTAR
(Now, Hubble’s instruments have built-in corrective optics, so COSTAR is no longer needed.)
Aperture of primary mirror: 2.4 m (~8 ft.)
Mass of primary mirror: 828 kg (~1800 lbs)

20. Summary Multiple Lenses The Eye Optical Instruments
The image of one lens is the object for the next lens.
The Eye
Corrective lenses place image of object at a point where person is able to view it, when he/she cannot properly focus on the object itself.
Optical Instruments
Use multiple lenses to build microscopes, telescopes, etc….
Text Reference: Chapter 34.2,4
Examples: 34.9,10,12,13,14 and 15