Physics
Physics
Problem
(i) For an object placed just beyond the focal point of the objective lens of a compound microscope, derive an expression for the linear magnification produced by the objective in terms of the tube length and the focal length of the objective. (ii) Using the result of part (i) together with the angular magnification of the eyepiece, obtain the expression for the overall magnifying power of the compound microscope when the final image is at infinity. (iii) Clearly state the approximations, if any, used at each stage of your derivation.Intuitive explanation
The key to a compound microscope is understanding that the objective creates a real, magnified intermediate image, which the eyepiece then views as a magnifying glass. For part (i), you'll use the lens equation and geometry to relate how far the intermediate image forms to the tube length and focal length—the closer the object sits to the focal point, the farther (and larger) that image becomes. Part (ii) combines this objective magnification with the eyepiece's angular magnification, recognizing that when the final image is at infinity, the eyepiece is in its most comfortable viewing mode and the intermediate image lands precisely at its focal point. Throughout, you'll need to identify where you assume small angles, neglect lens thickness, or treat the tube length as much larger than focal lengths.
Intuitive explanation
The key to a compound microscope is understanding that the objective creates a real, magnified intermediate image, which the eyepiece then views as a magnifying glass. For part (i), you'll use the lens equation and geometry to relate how far the intermediate image forms to the tube length and focal length—the closer the object sits to the focal point, the farther (and larger) that image becomes. Part (ii) combines this objective magnification with the eyepiece's angular magnification, recognizing that when the final image is at infinity, the eyepiece is in its most comfortable viewing mode and the intermediate image lands precisely at its focal point. Throughout, you'll need to identify where you assume small angles, neglect lens thickness, or treat the tube length as much larger than focal lengths.