An insect subtends an angle of only 4.0 ×10^-3 rad at the...

An insect subtends an angle of only $4.0 \times 10^{-3}$ rad at the unaided eye when placed at the near point. What is the angular size (magnitude only) when the insect is viewed through a microscope whose angular magnification has a magnitude of $160 ?$

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Key Concepts

Angular Size

Angular size refers to the angle an object subtends at the point of observation. It is a measure of how large the object appears to a viewer and depends on both the actual size of the object and its distance from the observer. This concept is important in optics because it helps in understanding how different viewing conditions or instruments affect the perceived size of an object.

Angular Magnification

Angular magnification is the factor by which an optical instrument, such as a microscope or telescope, increases the apparent angular size of an object. It is calculated as the ratio of the angle subtended by the image when viewed through the instrument to the angle subtended by the object when viewed with the naked eye. This concept is crucial in the design of optical devices to enhance the visibility of small or distant objects.

Near Point

The near point is defined as the shortest distance at which the human eye can focus on an object clearly, typically around 25 centimeters for a normal adult eye. It is used as a standard measure in optics and is often the reference point for calculating angular sizes and magnifications in both unaided and instrument-assisted vision.

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