A Huygens ocular is constructed of 2 thin lenses of focal length 10 cm and 5 cm, respectively, separated by 7

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104350
A Huygens ocular is constructed of 2 thin lenses of focal length 10 cm and 5 cm, respectively, separated by 7.5 cm. The ocular is used in an astronomical telescope whose objective is 30 cm to the left of the front lens of the ocular. What is the position of the exit pupil and what is the focal length of the ocular?

[The Huygens ocular is the combination of two plano convex lenses made of same material, the focal length of the field lens being three times that of the eye lens. The two lens are placed coaxially at a distance of 2f, where f is the focal length of eye lens and there curved surfaces are towards the incident light. The combination of lenses satisfies the condition of chromatic aberration as well as the spherical aberration is minimum.]

Answer:

The telescope used to see distant objects (for parallel incident rays) and the final image is also at infinity (the transmitted rays are parallel).

The image formed by objective I1 is the virtual object for the first lens of ocular. The image of this virtual object, I2 is the object for eye lens.

The distance between the eye lens L2 and the image I2 must be equal to the focal length 5.0 cm of eye lens in order to form the final image at infinity. Hence I2L2 = 5 cm. The distance of I2 from the first lens L1 will be 7.5 - 5.0 = 2.5 cm. which is the image distance for the first lens and hence using the lens formula with appropriate signs we can find the distance u between the first lens L1 and the image I1. Thus

or
Gives u = 10/3 cm.

Now as LoI1 is equal to the focal length of the objective 30.0 cm the distance of the first lens L1 from objective is

LoL1 = 30 - (10/3) = 26.67 cm

Hence the distance of the eye lens from the objective will be

LoL2 = 26.667 + 7.5 = 34.17 cm.

The focal length of ocular is given by

or cm