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In optics, where is the circle of least confusion located when using a +2.00 +1.00x90 lens?

20 cm behind the lens

40 cm behind the lens

The circle of least confusion refers to the smallest blur circle that occurs in an optically imperfect system, such as when using cylindrical lenses, which create astigmatism. In this case, when dealing with the given lens of +2.00 +1.00x90, it's a combination of spherical and cylindrical power.

To determine the location of the circle of least confusion, one must first assess the impact of the combined lens system. The spherical component of the lens (+2.00) contributes power uniformly across meridians, while the cylindrical component (+1.00 at 90 degrees) yields power in a specific direction. The concept is that the circle of least confusion lies halfway between the two focal lines produced by the spherical and cylindrical parts of the lens.

Since the positive power of the lens affects focal length inversely, the focal point of the +2.00 spherical component would typically be located at 50 cm from the lens (as focal length is the reciprocal of lens power), while the cylindrical component adds an additional layer of complexity based on its orientation and power.

By calculating the effective focal length based on the orientations and the combination of the powers, one can find that it results in a specific distance behind the lens where the circle

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60 cm behind the lens

80 cm behind the lens

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