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
Spherical and thin lenses
Spherical lens sculpture
s > 0
R > 0
s > 0
s = 14 cm
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
divergingExample: 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.
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
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
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
Where does the image of the arrow form?
Eye intercepts reflected rays that come from a point of the image on screen
If we place a screen
at image location
Converging or diverging image on screen“power” (in diopters = m-1 ):The formulae…
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