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__Magnifying Glass/Simple Microscope__ (image at **Near Point**)

**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 **h _{i}** divided by the height of the object

**h**:

_{o}

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

rearranging,

If we now use the lens equation:

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

Hence,

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

From our derivation of magnification **M** (above),

therefore our equation becomes,

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

where * f* is measured in

**centimetres**(

**cm**).

__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 **(I _{1}**) is positioned infront of the eyepiece, between f and the lens. The eyepiece produces the virtual image (

**I**) behind the first image.

_{2}

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** ( **M _{P} **) of a microscope is the

**product of the eyepiece**(

**M**) and

_{e}**objective lens magnification**(

**M**).

_{e }

**M _{P}** =

**M**x

_{e}**M**

_{o}

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