Q.Draw ray diagram of a compound microscope. Deduce an expression for its magnifying power when image is formed at near point.
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A compound microscope uses two convex lenses: the objective forms a real magnified image, which the eyepiece then further magnifies as a simple magnifier; the overall magnifying power multiplies the two stages' magnifications.
COMPOUND MICROSCOPE - CONSTRUCTION AND RAY DIAGRAM: it consists of two convex lenses mounted coaxially at the two ends of a tube: the OBJECTIVE (facing the object, small focal length f_o) and the EYEPIECE (facing the eye, focal length f_e, with f_e generally larger than f_o but both lenses being of short focal length).
The object AB is placed just beyond the focal point of the objective (u slightly greater than f_o). The objective forms a REAL, INVERTED, and MAGNIFIED image A'B' inside the tube, near the focal point of the eyepiece (in fact, for the final image at the near point, A'B' forms just inside the eyepiece's focal length f_e, i.e. between the eyepiece and its focus).
This real image A'B' now acts as the OBJECT for the eyepiece. Since A'B' lies within the eyepiece's focal length, the eyepiece works as a SIMPLE MAGNIFIER (magnifying glass), producing a final image A''B'' that is VIRTUAL, further MAGNIFIED, and (relative to A'B') ERECT - but since A'B' was already inverted relative to the original object AB, the final image A''B'' is INVERTED relative to the original object AB.
(Ray diagram description: two rays from the tip of object AB - one parallel to the principal axis, one through the objective's optical centre - are traced through the objective to locate the real, inverted, magnified image A'B'. Then two rays from the tip of A'B' are traced through the eyepiece [one parallel to the axis, refracted through F_e' of the eyepiece; one through the eyepiece's optical centre, undeviated] to locate the final, larger, virtual image A''B'', shown by dashed lines on the same side as A'B', at the near point.)
MAGNIFYING POWER (image at the near point D): The overall magnifying power M is the product of the magnification produced by the objective (m_o) and the magnifying power of the eyepiece as a simple magnifier (m_e):
M = m_o * m_e
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