Optical Instruments
Power of a lens
• Optometrists, instead of using focal length,
use the reciprocal of the focal length to
specify the strength of eyeglasses or
contact lenses. This is called power.
• P = f -1
Diopter (D)
• The unit for lens power is the diopter (D),
which is an inverse meter (m-1)
• For example, a 20. cm focal length lens
has a power of 1/(0.20 m) or 5.0 m-1.
Using the unit diopter, the power is written
as 5.0 D.
Linear Magnification
• Linear magnification is the ratio of the size
of an image to the size of an object. It will
be represented by a lower case m.
• m = hi/ho
The Eye
Near Point
• The closest distance at which the eye can
focus clearly is called the near point of
the eye. For young adults, the near point
is typically 25 cm. As people grow older,
the ability of the eye to accommodate is
reduced and the near point increases.
• * The focusing adjustment of the eye is
called accommodation.
Far Point
• A given person’s far point is the farthest
distance at which an object can be clearly
seen. For the normal eye, the far point
may be assumed to be at infinity.
Simple Magnifier
• One of the most basic optical devices
people use is a simple magnifier or
magnifying glass.
• How large an object appears depends on the
size of the image it makes on the retina.
• The size of the image made on the retina
depends on the angle subtended by the object
at the eye.
• When we want to examine an object in greater
detail, we bring it closer to our eye so that it
subtends a greater angle. However, our eyes
can only accommodate up to the near point of
25 cm.
• A magnifying glass allows us to effectively
place the object closer to our eye so that it
subtends a greater angle.
• * In order to produce a virtual image, the
object must be placed between f and the
lens.
Angular Magnification
• The angular magnification (M) of a lens
is defined as the ratio of the angle
subtended by the object when using the
lens to the angle subtended by the object
using the unaided eye (with the object
located at the near point N)
• M = Θ′/Θ
Magnification of Simple Magnifier
• We are interested in two extremes. When
the image is located at infinity and when
the image is located at the eye’s near
point.
Image located at infinity
• If the eye is relaxed, the object will be at
the focal point and the image at infinity.
• In this case, Θ′ = h/do = h/f and Θ = h/N
• Prove M = N/f
Image located at the near point
• The magnification of a given lens can be
increased slightly by moving the lens and
adjusting your eye so that it focuses on the
image at the eye’s near point.
• In this case, di = -N, Θ′ = h/do and Θ = h/N.
• Prove M = 1 + N/f
Practice Problem
• An 8. cm focal length lens is used by a
jeweler as a magnifying glass. Estimate
the angular magnification when (a) the eye
is relaxed (answer = 3) and (b) when the
eye is focused at its near point (answer =
4)
The Compound Microscope
Objective Lens and Eyepiece
• Both microscopes and telescopes make use of
an objective lens and an eyepiece.
• The objective lens is the lens closer to the
object. It has a focal length of fo and causes a
real image to be formed.
• The eyepiece (focal length fe) uses the image
formed by the objective lens as its object. The
eyepiece gives a virtual image that is larger than
the image formed by the objective lens.
Ray Diagram for a Compound
Microscope
Telescopes
• Several types of astronomical telescopes
exist. The common refracting type,
sometimes called Keplerian, contains two
converging lenses located at opposite
ends of a long tube.
Ray Diagram for an Astronomical
Telescope
Angular Magnification for
astronomical telescopes
• M = -f0/fe
Lens Aberrations
• When we learned about lens ray diagrams, we
made a couple of approximations that, in reality,
are not true.
• We assumed that all rays of light would be close
to the principal axis, and we assumed that light
would pass though the center of the lens without
bending.
• In reality, due to the true nature of lenses,
aberrations may occur that result in an imperfect
image.
Spherical Aberration
• Spherical aberration occurs because
spherical surfaces are not the ideal shape
with which to make a lens, but they are by
far the simplest shape to which glass can
be ground and polished and so are often
used. Spherical aberration causes beams
parallel to, but distant from, the lens axis
to be focused in a slightly different place
than beams close to the axis. This
manifests itself as a blurring of the image.
Spherical Aberration Diagram
Reducing Spherical Aberration
• Spherical aberration can be corrected by
using non-spherical lens surfaces.
However, to grind such a lens is
expensive.
• Spherical aberration is generally
minimized by using a series of lenses in
combination and only using the central
part of the lens.
Chromatic Aberration
• Spherical aberration will occur for
monochromatic light is called a
monochromatic aberration.
• Normal light, however is not
monochromatic, but contains all the
colours of the spectrum.
• Chromatic aberration occurs due to the
different colours of light passing through a
lens simultaneously.
• Chromatic aberration occurs because of
dispersion – the variations of index of
refraction with colour resulting in the
different colours of light bending different
amounts.
• For example, blue light bends more than
red light as it passes through a prism.
• So, if white light passes through a lens, the
different colours will focus at different
points. This is chromatic aberration.
Diagram showing chromatic
aberration
Eliminating Chromatic Aberration
• Chromatic aberration can be eliminated for
any two colours (and greatly reduced for
all others) by the use of two lenses made
of different materials with different indices
of refraction. Normally, one lens is
converging and one is diverging and they
are cemented together.
• This combination is called an achromatic
doublet.
Diagram for achromatic doublet