1 / 16

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

garnet
Download Presentation

Lecture 36

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related