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d o = d i

which is the same as [link] obtained earlier.

Notice that we have been very careful with the signs in deriving the mirror equation. For a plane mirror, the image distance has the opposite sign of the object distance. Also, the real image formed by the concave mirror in [link] is on the opposite side of the optical axis with respect to the object. In this case, the image height should have the opposite sign of the object height. To keep track of the signs of the various quantities in the mirror equation, we now introduce a sign convention.

Sign convention for spherical mirrors

Using a consistent sign convention is very important in geometric optics. It assigns positive or negative values for the quantities that characterize an optical system. Understanding the sign convention allows you to describe an image without constructing a ray diagram. This text uses the following sign convention:

  1. The focal length f is positive for concave mirrors and negative for convex mirrors.
  2. The image distance d i is positive for real images and negative for virtual images.

Notice that rule 1 means that the radius of curvature of a spherical mirror can be positive or negative. What does it mean to have a negative radius of curvature? This means simply that the radius of curvature for a convex mirror is defined to be negative.

Image magnification

Let’s use the sign convention to further interpret the derivation of the mirror equation. In deriving this equation, we found that the object and image heights are related by

h o h i = d o d i .

See [link] . Both the object and the image formed by the mirror in [link] are real, so the object and image distances are both positive. The highest point of the object is above the optical axis, so the object height is positive. The image, however, is below the optical axis, so the image height is negative. Thus, this sign convention is consistent with our derivation of the mirror equation.

[link] in fact describes the linear magnification    (often simply called “magnification”) of the image in terms of the object and image distances. We thus define the dimensionless magnification m as follows:

m = h i h o .

If m is positive, the image is upright, and if m is negative, the image is inverted. If | m | > 1 , the image is larger than the object, and if | m | < 1 , the image is smaller than the object. With this definition of magnification, we get the following relation between the vertical and horizontal object and image distances:

m = h i h o = d o d i .

This is a very useful relation because it lets you obtain the magnification of the image from the object and image distances, which you can obtain from the mirror equation.

Solar electric generating system

One of the solar technologies used today for generating electricity involves a device (called a parabolic trough or concentrating collector) that concentrates sunlight onto a blackened pipe that contains a fluid. This heated fluid is pumped to a heat exchanger, where the thermal energy is transferred to another system that is used to generate steam and eventually generates electricity through a conventional steam cycle. [link] shows such a working system in southern California. The real mirror is a parabolic cylinder with its focus located at the pipe; however, we can approximate the mirror as exactly one-quarter of a circular cylinder.

Questions & Answers

what is meant by fluctuated
Olasukanmi Reply
If n=cv then how v=cn? and if n=c/v then how v=cn?
Natanim
convert feet to metre
Mbah Reply
what is electrolysis
Mbah
Electrolysis is the chemical decomposition of electrolyte either in molten state or solution to conduct electricity
Ayomide
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Ayesha Reply
can someone help explain why v2/c2 is =1/2 Using The Lorentz Transformation For Time Spacecraft S′ is on its way to Alpha Centauri when Spacecraft S passes it at relative speed c /2. The captain of S′ sends a radio signal that lasts 1.2 s according to that ship’s clock. Use the Lorentz transformati
Jennifer
find a so that A=2i-3j+5k&B=3i+aj-2k orthogonal
Mulalem Reply
yes light it is form of energy
Gatkuoth Reply
yeah
SALONI
what's torque of force
Gatkuoth
torque=rFSintheta
SALONI
can you explain more on torque with this equation
RRGN
torque is actually the rotational equivalent of linear force....as this equation tells..... however in general terms it is the turning effect of applied force
ashwani
Torque is moment of Force if a force is applied at some finite distance from COM of a body it produce rotation. For pure rotation we need to apply Couple not Torque...
Researchers
what is the physics
Vinod Reply
the speed of light in a
amanuel Reply
what is an atom
Aroyameh Reply
All matter is composed of two sets of three dimensions. The first set (1,2,3) decay with a positive charge. The second set (4,5,6) decay with a negative charge. As they decay, they create space (7 8,9) dimensions.
John
Two sets of (1,2,3,4,5,6) dimensions create a proton, a neutron, and an electron. This is the primordial atom.
John
A 10kg mass lift to a height of 24m and release. what is the total energy of the system
ADEPOJU Reply
mechanics is that branch of physical and mathatics that
ADEPOJU
E=Mgh=10*10*24=2400J
Adamu
what is the difference between a molecule and atom
Natanim Reply
Atoms are single neutral particles. Molecules are neutral particles made of two or more atoms bonded together.
Manfred
what I'd dynamic propulsion
Elias Reply
A car travels 20KM due north of them 35KM is a direction 60° west to north. find the magnitude of direction of the car's resultant displacement?
Mulalem
A body quadruples its momentum when its speed doubles.What was the initial speed in units of c.i.e..what was u/c ?
Lekshmi Reply
what is enthalpy?
prabir Reply
a thermodynamic quantity equivalent to the total heat content of a system
RAMLA
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bloch
What is the meaning of Nuclear Fission?
Benita Reply
nuclear fission. are atom split apart which releases energy
Komolafe
what do you mean by dynamics single particles
Peacekamei Reply

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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