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Lecture 15
Refraction, Lenses, Aberrations
Chapter 23.4  23.7
• Atmospheric Refraction
• Thin Lenses
• Aberrations
Atmospheric Refraction
Atmospheric refraction is bending of light due to
gradual changing density of the air throughout the
Images of objects, close to the horizon, appear at a
higher elevation that the real objects are.
Atmospheric refraction is hardly noticeable at high
viewing angles (e.g., near zenith).
Atmospheric Refraction
The mirage is an atmospheric refraction phenomenon
due to large temperature changes of the air at different
heights above the Earth.
Light rays from an object move toward the observer
in two different ways through the different
temperature layers.
There are superior (inverted image above the ‘normal’)
and inferior (inverted image is below the ‘normal’).
Thin Lenses
A lens is a piece of glass (plastic) with two refracting
surfaces, which are either curved (e.g., a segment of
a sphere) or plain.
Lenses are used to form images by refraction in
optical instruments (microscopes, telescopes,
cameras, etc.)
Two types of lenses: converging (thickest in the
middle) and diverging (thickest at the edges).
Thin Lenses
The focal length of a lens is the image distance of
an object at an infinite distance from it.
The focal point is where a group of rays parallel to
the lens’ axis converges.
The thin-lens equation has the same form as the
mirror equation.
Lens maker’s equation
1 1
 = (n1)   
q f
R1 R2
Sign Convention
Ray Diagram for Thin Lenses
Ray 1: parallel to the lens’ axis, to its center,
through the focus on the other lens’ side.
Ray 2: through the lens’ center, continues in a
straight line.
Ray 3: through the closest focus, emerging from
the lens parallel to the lens’ axis.
Combinations of Thin Lenses
For a system of two lenses, the image formed by the
first one is treated as the object for the second one.
The image formed by the second lens is the final
image of the system.
The overall magnification is the product of the
magnifications of the individual lenses.
Problem with a Two-Lens System
Problem: Find the
image location.
p' = 12cm f '=  6cm
1 1
f ' p' q'
q' = 4cm
p = 12+4=16cm
f = 8cm
1/q = 1/81/16=1/16
q = 16cm
Departures of real images from the ideal predicted
by simple theory are called aberrations.
Types of aberrations
To reduce spherical aberration, parabolic mirrors
are used instead of spherical.
To reduce chromatic aberration, combinations of
converging and diverging lenses are used.
• Atmospheric refraction is a phenomenon that moves
images of objects, seen through the air, due to a
gradual change of the air density and temperature.
• Thin lenses are used to form images by refraction in
optical instruments to enhance our vision.
• Aberrations are distortions of images, predicted by
the simple theory of geometric optics.