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Lecture 36

Lecture 36. Spherical and thin lenses. Spherical lens sculpture. Thin lenses. Refraction in a spherical surface. n 1. n 2. h. s > 0. s ’ > 0. R > 0. Paraxial approximation. Magnification (spherical refracting surface). n 1. n 2. y. y ’. s > 0. s ’ > 0. s = 14 cm R = –14 cm

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Lecture 36

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  1. Lecture 36 Spherical and thin lenses Spherical lens sculpture Thin lenses

  2. Refraction in a spherical surface n1 n2 h s > 0 s’> 0 R > 0

  3. Paraxial approximation

  4. Magnification (spherical refracting surface) n1 n2 y y’ s > 0 s’> 0

  5. s = 14 cm R = –14 cm s’=–14 cm Or: Fish appears in the center but 33% larger! In-class example: Fish bowl A spherical fish bowl has a 28.0 cm diameter and a fish at its center. What is the apparent position and magnification of the fish to an observer outside of the bowl? A. s’ = –7 cm, m = 2.0 B. s’ = +7 cm, m = –2.0 C. s’ = –14 cm, m = 1.3 D. s’ = +14 cm, m = –1.3 E. s’ = –14 cm, m = 1.0

  6. Lenses: through two spherical surfaces nout nout Do the calculation twice, once for each surface. nin R1 R2 Overall effect (combination of nin, nout, R1and R2)

  7. Thin lens model • In this model • thickness of material <<distances to objects, images • angles tend to be small • consider doubly effective refraction at center of lens Everything can then be described in terms of two focal points: f: focal distance |f | |f | F2 F1

  8. Lensmaker’s equation If we analyze a thin lens in terms of the two spherical surfaces it is made of (in the paraxial approximation), we obtain: Proof: see book Remember: R > 0 if center of curvature is on the same side of surface as outgoing rays

  9. R1 R2 diverging Example: Diverging lens A double-concave lens is made of glass with n = 1.5 and radii 20 cm and 25 cm. Find the focal length. R1 = –20 cm R2 = +25 cm Note: If we reverse the lens (R1 = –25 cm and R2 = +20 cm), the result is the same.

  10. Principal rays Of the many possible rays you could draw, 3 are very useful • parallel to axis refracts through focus 2) through center (no net refraction due to symmetry) 3) through focus refracts parallel to axis

  11. DEMO: Converging lens Typical shapes: Converging lens Object at infinity forms a real image at F2 (observer sees rays appearing to originate from point F2) Focal length f > 0 Small |f| more converging

  12. DEMO: Diverging lens Typical shapes: Diverging lens Object at infinity forms a virtual image at F2 (observer sees rays as if coming from point F2) Focal length f < 0 Small |f| more diverging

  13. DEMO: Smiley on bulb. Example: Converging lens Where does the image of the arrow form? F F

  14. Eye intercepts reflected rays that come from a point of the image on screen If we place a screen at image location Diffuse reflection from screen F F

  15. Converging or diverging “power” (in diopters = m-1 ): The formulae… y F F y’ f f s s’ Valid for both convergent and diverging thin lenses (and mirrors) in the paraxial limit

  16. Example: Diverging lens Where is the image if this is a lens of -10 diopters? 30 cm Virtual, smaller, upright image

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