# If we have a focus f1 = 1 cm (Microscope Lenses) and f2 = 2 cm (eyepiece) and the distance of the object a1 = 1.2cm, how to find a2?

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### 1 Answer

See the image attached for how the light rays travels through a microscope.

In a microscope the objective (which have a focal lens of `f1`) is forming a real and inverted image of the object. This image is then taken as an object by the eyepiece (which have a focal lens of `f2`). In a microscope the arrangement of the distances is in such a way that` ` the image formed by the objective (that acts as an object for the eyepiece) is about in the focal point of the eyepiece. (This is why people need to adjust the microscope tube length.) Thus the final image formed is larger and non-inverted, formed by the eye-piece at about an infinite distance.

The distances are shown in the figure.

For the objective we have the following equation

`1/a_1 +1/a_2 =1/f_1`

where `a_1>0` to the left of lens, `a_2>0` to the right of lens and `f>0` .

`1/a_2 =1/f_1 -1/a_1 =1/1 -1/1.2 =0.167`

`a_2 = 6 cm`

For the eyepiece we have the following equation

`1/a_1' +1/a_2'=1/f_2`

with the same conventions as above.

Here as explained `a_1' =f_2` , therefore

`1/a_2' =0` or equivalent `a_2' =-oo or +oo`

In reality the image produced by the eyepiece is a bit closer than `-oo` but still very far from it.

**The image produced by the objective is at 6 cm distance to the right of the objective and the final image produced by the eyepiece is at infinity to the left of the eyepiece.**

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