Question

Draw a suitable ray diagram of a compound microscope, when the image is formed at the least distance of distinct vision. Find the expression of magnifying power in this case.

Hint:

The total magnification of a compound microscope depends on both the focal length of the objective lens and the eyepiece.

Answer 1

Step 1: Ray Diagram for Compound Microscope.
The compound microscope consists of an objective lens (converging lens) and an eyepiece. The object is placed at a distance \( u_o \) such that the image formed by the objective lens is at the focus of the eyepiece.

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Step 2: Magnifying Power.
The magnifying power \( M \) of a compound microscope is given by the product of the magnifying powers of the objective lens and the eyepiece: \[ M = M_{\text{obj}} \times M_{\text{eye}} \] where: - \( M_{\text{obj}} = \frac{v_o}{u_o} \) is the magnification produced by the objective lens, - \( M_{\text{eye}} = \frac{D}{f_e} \) is the magnification produced by the eyepiece, where \( D \) is the least distance of distinct vision (usually taken as \( 25 \, \text{cm} \)) and \( f_e \) is the focal length of the eyepiece. For the compound microscope, the total magnification is given by: \[ M = \frac{D}{f_o} \times \frac{25}{f_e} \] where \( f_o \) is the focal length of the objective lens and \( f_e \) is the focal length of the eyepiece.
Step 3: Conclusion.
The magnifying power of the compound microscope when the image is formed at the least distance of distinct vision is given by: \[ M = \frac{D}{f_o} \times \frac{25}{f_e} \]