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Optics: vocabulary and calculus
Aperture: (of a telescope, a camera, a microscope...) to be correct, the aperture is a dimensionless number: it is
the ratio between the diameter diaphragm (where the light comes in) and the focal distance of the objective. The
higher it is, the more light you can collect with the device.
It is often confounded with the diameter of the diaphragm alone.
Eyepiece: the eyepiece of an optical device (microscope, telescope...) is the lens you actually look through.
Field of view: (of an optical device) region of space where objects must be to give an image through this optical
device
Magnification
Magnification is the process of enlarging something only in appearance, not in physical size. This
enlargement is quantified by a calculated number also called magnification.
Optical magnification is the ratio between the apparent size of an object (or its size in an image) and its
true size, and thus it is a dimensionless number.
a) Linear or transverse magnification: for real images, such as images projected on a screen, size means a
linear dimension (measured, for example, in millimetres or inches).
b) Angular magnification: for optical instruments with an eyepiece, the linear dimension of the image seen
in the eyepiece (virtual image in infinite distance) cannot be given, thus size means the angle subtended
by the object at the focal point (angular size). Strictly speaking, one should take the tangent of that angle
(in practice, this makes a difference only if the angle is larger than a few degrees). So angular
magnification is the ratio between the two angles instead of the two sizes.
Example: The angular size of the full moon is 0.5°, in binoculars with 10x magnification it appears to
subtend an angle of 5°.
When this number is less than one it refers to a reduction in size, sometimes called minification or demagnification. When this number is negative, it means that image is upside down compared to the object.
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Draw the image and calculate magnifications (literal formula and numeric value)
Linear magnification M =
Angular magnification MA=
Remark: if two optical systems are put one after another, the total magnification is M1 M2
With any telescope or microscope, there is a maximum magnification beyond which the image looks bigger but
shows no more detail. It occurs when the finest detail the instrument can resolve is magnified to match the
finest detail the eye can see.
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Optical path: (of an optical device) the way the light is following in this device.
“Galileo’s telescope, the instrument that changed the world”
(actual title of a Galileo-dedicated website of the Museum of History of Science, Florence)
Introduction:
The science of astronomy took a huge leap forward in the first decade of the 1600s
with the invention of the optical telescope and its use to study the night sky. Galileo Galilei
did not invent the telescope but was the first to use it systematically to observe celestial
objects and record his discoveries.
His book, Sidereus nuncius or The Starry Messenger was first published in 1610 and
made him famous. In it he reported on his observations of the Moon, Jupiter and the Milky
Way.
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Galileo's Telescopes
The basic tool that Galileo used was a crude
refracting telescope. His initial version only magnified 8x
but was soon refined to the 20x magnification he used for
his observations for Sidereus nuncius. It had a convex
objective lens and a concave eyepiece in a long tube. The
main problem with his telescopes was their very narrow
field of view, typically about half the width of the Moon.
Galileo's drawings of phases of the Moon
Galileo's drawing of the optical path of his telescope
One of Galileo's telescopes . It has an objective bi-convex lens
and a plano-concave eyepiece. It magnifies 14.
Moons of Jupiter
Observations of the planet Jupiter over successive nights revealed four star-like objects in a line with it.
The objects moved from night to night, sometimes disappearing behind or in front of the planet. Galileo
correctly inferred that these objects were moons of Jupiter and orbited it just as our Moon orbits Earth. For the
first time, objects had been observed orbiting another planet, thus weakening the hold of the Ptolemaic model.
Today these four moons are known as the Galilean satellites: Io, Europa, Ganymede and Callisto.
Galileo's drawings of the moons of Jupiter over successive nights
The Phases of Venus
Venus was observed to go through a sequence of phases similar to the Moon. This could not be explained in the
Ptolemaic model but could be accounted for by either the Sun-centered Copernican model or the Earth-centered
Tychonic model that had the other planets orbiting the Sun as it orbited the Earth. Galileo rejected Tycho's
model as an unnecessary hybrid and used the discovery to consolidate his support of the Copernican model.
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Questions:
a) What features did Galileo discover on the surface of the Moon that cannot be seen with naked eye?
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b) According to Aristotelian principles “the Moon was above the sub-lunary sphere and in the heavens, hence
should be perfect”. What did Galileo's observations of the Moon reveal?
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c) Why did the telescope allow seeing objects that were invisible before? Which objects did Galileo discover?
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d) How did Galileo's observations help undermine the existing paradigm of the Ptolemaic model of the
Universe and Aristotle's physics?
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Other useful notes/vocabulary :
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