Question

If $f$ is the focal length of lens in Ramsden’s eyepiece, then cross wires are placed:
A. $\dfrac{f}{3}$ distance behind the field lens
B. $\dfrac{f}{3}$ distance in front of the field lens
C. $\dfrac{f}{4}$ distance in front of the field lens
D. $\dfrac{f}{4}$ distance behind field lens

Answer 1

An eyepiece is used in the optical instruments and acts as a simple magnifier. This reduces the aberration due to the lens. A Ramsden eyepiece also reduces the chromatic and spherical aberration due to the spacing of the lenses.

Complete answer:
Ramsden eyepiece consists of two plano-convex lense, which are placed facing each other. These lenses have similar focal length and are made of the same glass material, mostly spectacle crown glass. Here the focal length of the two lenses is the same and also, they are separated at a distance equal to two-third the focal length, from each other. We also know that the distance between the lens and the cross-wire is given as one-fourth the focal length.

Here, it is given that $f$ is the focal length of the lens in Ramsden’s eyepiece, then we can say that the distance between the two lenses is also $\dfrac{2}{3}f$. Then the distance between the lens and the cross-wire will be, $\dfrac{1}{4}f$.
Then the answer is either C or D
Since the eye in front of the lens as shown in the image above, we can say that the cross-wire must be behind the lens to avoid any disturbance in the vision.

Then, the answer is D.$\dfrac{f}{4}$ distance behind the field lens.

Note:
There are three types of the eyepiece namely, the Ramsden eyepiece as discussed above, orthoscopic eyepiece, where the field of view is wide and the magnification is high and the Erfle eyepiece, this is used in the astronomical telescopes due to its high quality.