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Huygens Eyepiece

This eyepiece is achromatic and the spherical aberration is also eliminated. It consists of two lenses having focal lengths in the ratio 3 : 1 and the distance between them is equal to the difference in their focal lengths. The focal lengths and the positions of the two lenses are such that each lens produces and equal deviation of the ray and the system in achromatic.

Suppose the field lens and the eye of focal lengths ƒ₁ and ƒ₂ are placed D cm apart. If F is the focal length of the combination,

Differentiating

As the dispersive power

For achromatism, ω/F = 0

Also, for equal deviation of a ray by the two lenses, the distance between the two lenses should be equal to ƒ₁ – ƒ₂.

Thus, to satisfy both the conditions, Huygens constructed an eyepiece consisting of two plano-convex lenses of focal lengths 3ƒ and ƒ placed at a distance 2ƒ from each other.

II₁ is the image of the distant object formed by the objective in the absence of the field lens. With the field lens, the rays get refracted on passing through it and the image I’I’₁, is formed. This image lies at the focus of the eye lens so that the final image is seen at infinity.

In the modern design, the focal lengths of the lenses are 2ƒ and ƒ placed at a distance of 1.5 ƒ from each other.

The focal length of the combination

The equivalent lens must be placed behind the field lens at a distance

i.e. 3ƒ from the field lens or at a distance ƒ behind the eye lens.

Huygens eyepiece is known as the negative eyepiece because the real inverted image formed by the objective lies behind the field lens and this image acts as a virtual object for the eye lens. This eye-piece cannot be used to examine directly an object or a real image formed by the objective. The eyepiece is used in microscope or other optical instruments using white light only.

Moreover, the cross wires must be placed (if the measurement of final image is required) between the field lens and the eye lens. But the cross wires are viewed through the eye lens only while the distant object is viewed by rays refracted through both the lenses. Due to this reason relative lengths of the cross wires and the image are disproportionate. Hence cross wires cannot be used in a Huygens eyepiece and this is a disadvantage. Hence, Huygens eyepiece cannot be used in telescopes and other optical instruments with which distance and angles are to be measured.