EP118 Optics. Content TOPIC 9 ABERRATIONS. Department of Engineering Physics University of Gaziantep. 1. Introduction. 2. Spherical Aberrations

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Introduction 2. Spherical Aberrations 3.

1 EP118 Optics TOPI 9 ABERRATIONS Department o Engineering Physics Uniersity o Gaziantep July 2011 Saya 1 ontent 1. Introduction 2. Spherical Aberrations 3. hromatic Aberrations 4. Other Types o Aberrations 5. Exercises 6. Reerences Saya 2 1

2 9.1 Introduction In an ideal optical system, all rays o light rom a point in the object plane would conerge to the same point in the image plane, orming a clear image. The inluences which cause dierent rays to conerge to dierent points are called aberrations. Aberration leads to blurring o the image produced by an image-orming optical system. It occurs when light rom one point o an object ater transmission through the system does not conerge into (or does not dierge rom) a single point. Optical Instrument-makers need to correct optical systems to compensate or aberration. In this chapter, we will consider spherical and chromatic aberrations and their corrections. Saya Spherical Aberrations (SA) Spherical aberrations occur because the ocal points o rays ar rom the principal axis o a spherical lens (or mirror) are dierent rom the ocal points o rays o the same waelength passing near the axis. Figures gien below illustrate spherical aberrations or parallel rays passing through a conerging lens, and relecting rom a concae mirror. Rays are conerged to dierent points instead o a single ocal point. Saya 4 2

3 Spherical aberration can be reduced by a screening method. To do this, a screen (pupil) can be placed in ront o the mirror or lens allowing parallel rays to ocus on a single point. NOTE THAT Screening reduces the brightness (light intensity) o the image while it reduces the spherical aberrations. Many cameras hae an adjustable aperture to control light intensity and reduce spherical aberration. Saya 5 EXAMPLE 1 A ray traeling parallel to the principal axis strike a conex mirror whose radius o curature is R = 25 cm as shown in Figure. Assume that the ray is at distances h = 5 cm. Find the angle θ. SOLUTION Saya 6 3

To oercome the spherical aberration in mirrors, parabolic relecting surace rather than a

Parallel light rays incident on a parabolic surace ocus at a common point, regardless o

Parabolic relecting suraces are used in many astronomical telescopes to enhance image

4 To oercome the spherical aberration in mirrors, parabolic relecting surace rather than a spherical surace is used. Parabolic suraces are not used oten --> ery expensie to make. Parallel light rays incident on a parabolic surace ocus at a common point, regardless o their distance rom the principal axis. Parabolic relecting suraces are used in many astronomical telescopes to enhance image quality. One can proe why we need parabolic relecting surace (See Appendix at the end) Saya 7 A parabolic solar dish The mirror o the Hubble Space Telescope Saya 8 4

5 9.3 hromatic Aberrations (A) A lens will not ocus dierent colors in exactly the same place. A occurs because lenses hae a dierent reractie index or dierent waelengths o light (the dispersion o the lens). c n( ) iolet red Saya 9 EXAMPLE 2 Figure shows a bi-conex lens o same radius (R = 10 cm) made up o a dense lint SF10. Determine the distance (x) between ocal length o the iolet and red lights i the lens is illuminated by a white light. SOLUTION Saya 10 5

like lint glass can correct the chromatic aberration or two colors, e.g., red and blue.

6 One way to minimize this aberration is to use glasses o dierent dispersion in a doublet or other combination. The use o a strong positie lens made rom a low dispersion glass like crown glass coupled with a weaker high dispersion glass like lint glass can correct the chromatic aberration or two colors, e.g., red and blue. Such doublets are oten cemented together and called achromat. An achromatic lens (or achromat) is designed to limit the eects o chromatic and spherical aberration. Saya 11 Saya 12 6

EXAMPLE 3 Figure shows an achromatic lens consisting o a crown glass BK7 (bi-conex conerging lens o same radius), and an unknown glass (plano-concae dierging lens). Lenses are cemented together.

7 EXAMPLE 3 Figure shows an achromatic lens consisting o a crown glass BK7 (bi-conex conerging lens o same radius), and an unknown glass (plano-concae dierging lens). Lenses are cemented together. The reractie indices o some materials as a unction o waelength are gien igure. Both lenses hae the same radius o curature R. Find the best unknown material such that ocal points o the red and iolet are the same or achromat lens. iolet red Saya 13 SOLUTION From the igure we can roughly ind the reractie index or red and iolet or red iolet the crown glass (BK7) as n 1.51 and respectiely. n Saya 14 7

EXAMPLE 4 Figure shows an achromatic lens consisting o a crown glass BK7 (bi-conex conerging lens o same radius), and lint glass F2 (plano-concae dierging lens).

8 EXAMPLE 4 Figure shows an achromatic lens consisting o a crown glass BK7 (bi-conex conerging lens o same radius), and lint glass F2 (plano-concae dierging lens). Their reractie indices as a unction o waelength are gien below. Lenses are separated by a distance x. Both lenses hae the same radius o curature R = 10 cm. Find a alue o x such that the ocal points o the red and iolet are the same. iolet red Saya 15 SOLUTION From the igure we can roughly ind the reractie index as ollows: Lens Reractie index (n) Red(700 nm) Violet(380 nm) rown Flint Applying Lens Maker s Equation or both lenses yields: For crown glass r R / 2 1 n R / 2 10/ cm n r R / 2 10/ cm n and or lint glass r F F F R 1 n F R cm n r F R cm n F Saya 16 8

Now we can calculate the ocal length o the compound lens system. The distance rom lint lens to the new ocus as unction o x or both waelength can be as ollows: r r r F ( x ) ( 16.

6 14.9x x) x ( ) x (9.3 14.9) x 5.6 ( F 0 160.7 16.4x 138.6 14.9x x 6.6 x 5.6 x 0.53 cm or x 18.53 cm Saya 17 9.

9 Now we can calculate the ocal length o the compound lens system. The distance rom lint lens to the new ocus as unction o x or both waelength can be as ollows: r r r F ( x ) ( 16.4)( x 9.8) x ( x) r r x ( ) x ( ) x 6.6 The aim is to ind a alue o x minimizing the distance between two ocal r points: That is F F ( x ) ( 14.9)( x 9.3) x x) x ( ) x ( ) x 5.6 ( F x x x 6.6 x 5.6 x 0.53 cm or x cm Saya Other Types o Aberrations Distortion is a deiation rom rectilinear projection. oma reers to aberration due to imperection in the lens Astigmatism is one where rays that propagate in two perpendicular planes hae dierent ocal lengths. Saya 18 9

10 Appendix: Deriation o parabolic surace. Saya Exercises 1. Does the image ormed by a plane mirror suer rom any aberration? 2. What are spherical and chromatic o aberrations? 3. Explain how can the spherical and chromatic aberrations be reduced? 4. The magnitudes o the radii o curature are 30 cm and 40 cm or the two aces o a biconcae lens. The glass has index o reraction 1.54 or iolet light and 1.50 or red light. For a ery distant object, locate and describe (a) the image ormed by iolet light, and (b) the image ormed by red light. 5. In EXAMPLE 1, ind an expression or the ocal length (extension o the ray relected on principle axis) o the mirror as a unction o h. 6. Repeat EXAMPLE 4 or LaSF9 and FK51A glasses. Saya 20 10

7. A light ray traeling parallel to the principal axis at a distance y rom the principal axis strike a concae mirror haing a radius o curature R as shown. The ray is ocused on point S such that OS =.

11 7. A light ray traeling parallel to the principal axis at a distance y rom the principal axis strike a concae mirror haing a radius o curature R as shown. The ray is ocused on point S such that OS =. (a) Find an expression or in terms o y and R. (b) What is the alue o when R >> y? onclude the result. Hint: tan2θ = 2tanθ/(1 tan2θ) 8. (Serway 6th Edition re[1]) Two rays traeling parallel to the principal axis strike a large plano-conex lens haing a reractie index o 1.6. I the conex ace is spherical, a ray near the edge does not pass through the ocal point (spherical aberration occurs). Assume this ace has a radius o curature o 20.0 cm and the two rays are at distances h1 = 0.5 cm and h2= 12.0 cm rom the principal axis. Find the dierence Δx in the positions where each crosses the principal axis. Saya Two lenses made o kinds o glass haing dierent reractie indices n 1 and n 2 are cemented together to orm what is called an optical doublet. Optical doublets are oten used to correct chromatic aberrations in optical deices. The irst lens o a doublet has one lat side and one concae side o radius o curature R. The second lens has two conex sides o radius o curature R. Show that the doublet can be modeled as a single thin lens with a ocal length described by: R 2n2 n1 1 Saya 22 11

12 9.6 Reerences 1. Serway, Beichner, Physics or Scientists and Engineers 6th ed, Brooks/ole 2. Karaali S., Geometrik Optik, Ege Uniersitesi Basımei 3. Ertaş İ., Denel Fizik Dersleri ilt II, Ege Üniersitesi Basımei Saya 23 12

Physics 142 Lenses and Mirrors Page 1. Lenses and Mirrors. Now for the sequence of events, in no particular order. Dan Rather

Physics 142 Lenses and Mirrors Page 1 Lenses and Mirrors Now or the sequence o events, in no particular order. Dan Rather Overview: making use o the laws o relection and reraction We will now study ormation