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magnifying glass

compound microscope




Magnifying Glass/Simple Microscope (image at Near Point)



ray diagram for a magnifying glass



D is the Near Point of the eye. This is the closest an object can be to the eye and remain in focus.


By definition, magnification M is the height of the image hi divided by the height of the object ho :


magnifying glass equation #1


From the diagram, the angle β (beta) is given by:


        magnifying glass equation #2



magnifying glass equation #4



If we now use the lens equation:


the lens equation


In this case, v = - D . The image is virtual. So the sign is negative.



magnifying glass equation #5


Multipling both sides by D, and taking the second term over to the right,


        magnifying glass equation #6


From our derivation of magnification M (above),


magnifying glass equation #7


therefore our equation becomes,


magnifying glass equation #8


With the image at the near point, the magnification of an object by a magnifying glass can be simplified as:


magnifying glass equation #9


where f is measured in centimetres (cm).



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Compound microscope



ray diagram for a compound microscope




A microscope is very similar in arrangement to a telescope, the difference being in the focal length of the objective lens.


Microscope lens focal lengths are measured in mm, while telescope focal lengths can be measured in metres.


Essentially a real image is formed by the objective and this in turn is magnified by the eyepiece to form a virtual, erect image.


The first image (I1) is positioned infront of the eyepiece, between f and the lens. The eyepiece produces the virtual image (I2) behind the first image.


For the second image to be in focus, the distance between it and the eye must be at least 25 cm (D).



The Magnifying Power ( MP ) of a microscope is the product of the eyepiece ( Me ) and objective lens magnification ( Me ).


MP = Me x Mo




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