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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Spherical and thin lenses
Spherical lens sculpture
s > 0
R > 0
s > 0
R = –14 cm
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
Do the calculation twice, once for each surface.
(combination of nin, nout, R1and R2)
Everything can then be described in terms of two focal points:
f: focal distance
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
R > 0 if center of curvature is on the same side of surface as outgoing rays
Of the many possible rays you could draw, 3 are very useful
2) through center (no net refraction due to symmetry)
3) through focus refracts parallel to axis
If we place a screen
at image location
Valid for both convergent and diverging thin lenses (and mirrors) in the paraxial limit
Where is the image if this is a lens of -10 diopters?
Virtual, smaller, upright image