In Huygen’s eyepiece, the distance between the two lenses is ‘P’, the effective focal length is ‘Q’, the focal length of field lens is ‘R’ and focal length of eye lens is ‘S’ then
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Answer:
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.
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.
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.
Answer:
This eyepiece is achromatic, which eliminates spherical aberration. It is made up of two lenses with focal lengths in the ratio 3: 1 and a distance between them equal to the focal length difference. The focal lengths and placements of the two lenses are such that each lens creates an equal achromatic ray deviation and system.
For achromatism, ω/F = 0
Also, the distance between the two lenses should be equal to ƒ1 – ƒ2. for equal ray deviation by the two lenses.
Huygens created an eyepiece consisting of two plano-convex lenses with focal lengths of 3ƒ and positioned at a distance of 2ƒfrom each other to meet both criteria.
In the absence of a field lens, II1 is the image of a distant object created by the objective. When rays travel through the field lens, they are refracted and the image I'I'1 is created. The final picture is seen at infinity because this image is at the focus of the eye lens.
The focal lengths of the lenses are 2ƒ in the current design, and ƒ they are located 1.5ƒ distance apart.
Because the true inverted image generated by the objective is behind the field lens and operates as a virtual object for the eye lens, the Huygens eyepiece is known as the negative eyepiece. This eyepiece can't be utilized to look at an object or a genuine picture created by the objective directly. The eyepiece is exclusively used in white light microscopes and other optical devices.
Furthermore, cross wires must be put between the field lens and the eye lens (if final image measurement is necessary). The cross wires, on the other hand, are only seen through the eye lens, whilst the distant object is visible by rays refracted through both lenses. As a result, the cross wires' and image's relative lengths are disproportionate. As a result, cross wires cannot be employed in a Huygens eyepiece, which is a drawback. As a result, Huygens eyepieces cannot be used in telescopes or other optical equipment that measure distances and angles.