What is a compound microscope? Explain its construction with the help of a figure.

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(N/A) simple microscope has a limited maximum magnification $(\leq 9)$ for realistic focal lengths. For much larger magnification,one uses two lenses,one compounding the effect of the other. This is known as a compound microscope.
$A$ schematic diagram of a compound microscope is shown in the figure.
The lens nearest the object,called the objective,forms a real,inverted,and magnified image of the object.
This image serves as the object for the second lens,the eyepiece,which functions essentially like a simple microscope or magnifier,producing the final image which is enlarged and virtual.
The first inverted image is thus near (at or within) the focal plane of the eyepiece at a distance appropriate for final image formation at infinity,or a little closer for image formation at the near point. Clearly,the final image is inverted with respect to the original object.

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If the focal length of the objective and eye lens are $1.2 \, cm$ and $3 \, cm$ respectively,and the object is placed $1.25 \, cm$ away from the objective lens,and the final image is formed at infinity,the magnifying power of the microscope is:

Which of the following statements are true in the context of a Compound Microscope?
$(A)$ The objective lens forms a virtual and magnified image.
$(B)$ The objective lens has a very short focal length.
$(C)$ The eyepiece acts as a simple magnifying glass.
$(D)$ The eyepiece is a concave lens.

The focal lengths of the objective and eye-lens of a microscope are $1 \,cm$ and $5 \,cm$ respectively. If the magnifying power for the relaxed eye is $45$,then the length of the tube is $....... \,cm$.

Answer the following questions:
$(a)$ The angle subtended at the eye by an object is equal to the angle subtended at the eye by the virtual image produced by a magnifying glass. In what sense then does a magnifying glass provide angular magnification?
$(b)$ In viewing through a magnifying glass,one usually positions one's eyes very close to the lens. Does angular magnification change if the eye is moved back?
$(c)$ Magnifying power of a simple microscope is inversely proportional to the focal length of the lens. What then stops us from using a convex lens of smaller and smaller focal length and achieving greater and greater magnifying power?
$(d)$ Why must both the objective and the eyepiece of a compound microscope have short focal lengths?
$(e)$ When viewing through a compound microscope,our eyes should be positioned not on the eyepiece but a short distance away from it for best viewing. Why? How much should be that short distance between the eye and eyepiece?

What is the magnifying power of a simple microscope of focal length $5 \ cm$,if the image is formed at the distance of distinct vision?

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