A microscope has an objective lens with a focal length of...

A microscope has an objective lens with a focal length of 16.22 mm and an eyepiece with a focal length of 9.50 mm. With the length of the barrel set at 29.0 cm, the diameter of a red blood cell’s image subtends an angle of 1.43 mrad with the eye. If the final image distance is 29.0 cm from the eyepiece, what is the actual diameter of the red blood cell? Hint: To solve this question, go back to basics and use the thin-lens equation.

Key Concepts

Angular Magnification and Subtended Angle

Angular magnification refers to the relationship between the angular size of an image as seen by the observer and the actual angular size of the object. In optical systems, the subtended angle measured (often in radians for small angles) can be linked back to the physical size of the object via distance measurements according to basic trigonometric approximations (? ? size/distance for small angles). This concept is essential when determining actual sizes from the perceived angular dimensions of an image.

Thin-Lens Equation

The thin-lens equation, 1/f = 1/d_o + 1/d_i, is fundamental in geometric optics. It relates the focal length of a lens to the distances of the object (d_o) and its corresponding image (d_i) from the lens. This equation allows one to determine where an image will form given an object distance and the lens’s focal length, and is instrumental in understanding image formation in optical instruments like microscopes.

Compound Microscope

A compound microscope is an optical instrument that uses a system of lenses—typically an objective and an eyepiece— to magnify small objects. The objective lens produces a real, inverted, and magnified image of the specimen, which is then further enlarged by the eyepiece to produce a final virtual image that can be observed by the eye. Understanding the role of each lens and their contribution to the overall magnification is crucial for solving related problems.

Magnification in Optical Systems

Magnification in optical systems such as microscopes is achieved by the combined action of the objective and the eyepiece. The overall magnification is determined by multiplying the magnifications provided by each lens. This concept allows one to relate the dimensions of the image to the real object, thereby enabling calculations of object size using the measured angular size and related distances in the microscope setup.

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