You have found in the lab an old microscope, which has lost...

You have found in the lab an old microscope, which has lost its eyepiece. It still has its objective lens, and markings indicate that its focal length is $7.00 \mathrm{~mm}$. You can put in a new eyepiece, which goes in $20.0 \mathrm{~cm}$ from the objective. You need a magnification of about 200 . Assume you want the comfortable viewing distance for the final image to be $25.0 \mathrm{~cm}$. You find in a drawer eyepieces marked $2.00-, 4.00-,$ and $8.00-\mathrm{cm}$ focal length. Which is your best choice?

Key Concepts

Compound Microscope

A compound microscope is an optical instrument that uses two lens systems—an objective lens and an eyepiece—to produce a highly magnified image of a small object. The objective creates a real, magnified image which is then further enlarged by the eyepiece, and the overall magnification is the product of the individual magnifications of these two lenses.

Focal Length and Image Formation

The focal length of a lens is the distance from the lens at which parallel rays converge to a point. It is a key parameter in image formation; in optical instruments, the focal length determines how much an object can be magnified, as the distance between the lens and the image plane relative to the focal length influences the size and clarity of the image.

Angular Magnification and Near Point

Angular magnification refers to the increase in the angle subtended by an image at the eye, compared to the angle subtended by the object viewed directly. In many optical devices, especially eyepieces, the angular magnification is approximated by the ratio of the near point distance (commonly taken as 25 cm for comfortable viewing) to the focal length of the eyepiece.

Design Trade-Offs in Optical Instruments

When designing optical instruments like microscopes, it is crucial to balance the contributions of the objective and eyepiece. The objective provides the initial magnification based on its focal length and the separation from the eyepiece, while the eyepiece provides additional angular magnification. The careful selection of each component ensures that the overall magnification meets the desired specification without compromising viewing comfort.

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