Compound-Microscope

Description:

Compound microscope is made up of two convex lenses. The convex lens that is close to the object is known as objective lens and the lens placed near to the eye is known as eye piece.

Objective lens has small focal length and small aperture because for small focal length it is necessary to have small aperture.

Eye piece has the same behavior as that of simple microscope.

While using compound microscope, object should be placed slightly outside the focus.

Consider an object AB is placed on the principle axis at a distance slight away from the focus of the objective lens. We consider two rays from the object, first ray is incident parallel to the principle axis and passes through focus after refraction while the second ray is directed towards the optical center and it passes without deviation.

These two rays intersect and form a real image A′B′.

This image acts as an object for the other lens (eye piece). We will again consider two rays that are incident on the lens. First ray is incident parallel to the principle axis and passes through focus after refraction while the second ray is directed towards the optical center and it passes without deviation

These two rays are diverging so they will not intersect i.e. real image will not be formed, but when these rays are drawn back they seem to intersect and form a virtual image A"B".

If the image distance is equal to the least distance of distinct vision (D) then the image will be extremely clear and sharp.

Magnification of the microscope is given by −

Magnification = Size of Image/Size of Object

∴ m = A"B"/AB

This equation can be adjusted as −

m = A"B"/A′B′ × A′B′/AB

As we can observe from figure, A"B" is the image generated by eye-piece and A′B′ is the object for eye-piece.

Similarly A′B′ is the image generated by objective lens and AB is the object for objective lens.

∴ m_M = m_e × m₀

Where,

m_M = Magnification for eye-piece.

m₀ = Magnification for objective lens.

Now, we have −

m_e = 1 + D/f_e

And

m₀ = v₀/u₀

Therefore magnification for compound microscope is given by −

m_M = (1 + D/f_e)(v₀/u₀)

∴ m_M = v₀/u₀(1 + D/f_e)

Roughly v₀ is equal to the total length of microscope L and u₀ is equal to the focal length of objective lens f₀

∴ m_M ≈ L/f₀(1 + D/f_e)

In the case of parallel rays (relaxed eye) −

m_M = v₀/u₀ × D/f_e

∴ m_M ≈ LD/f₀f_e

Where,

L = Length of microscope.

D = Least distance of distinct vision.

f₀ = Focal length of objective lens.

f_e = Focal length of eye-piece.