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(A) The total magnification $M$ of a compound microscope when the final image is formed at the least distance of distinct vision $(D = 25 \ cm)$ is gi

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$4$

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(A) The total magnification $M$ of a compound microscope when the final image is formed at the least distance of distinct vision $(D = 25 \ cm)$ is given by the formula: $M = m_o 	imes m_e$, where $m_o$ is the magnification of the objective and $m_e$ is the magnification of the eyepiece.For an eyepiece acting as a simple magnifier, the magnification $m_e$ is given by: $m_e = (1 + D/f_e)$.Given $D = 25 \ cm$ and $f_e = 5 \ cm$, we calculate $m_e = (1 + 25/5) = (1 + 5) = 6$.Given the total magnification $M = 24$, we substitute the values into the formula: $24 = m_o 	imes 6$.Solving for $m_o$, we get $m_o = 24 / 6 = 4$.Therefore, the magnification produced by the objective is $4$.

The total magnification produced by a compound microscope is $24$ when the final image is formed at the least distance of distinct vision. If the focal length of the eyepiece is $5 \ cm$, the magnification produced by the objective is

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