Going beyond the telescope

Classical Mechanics Level 4

Imagine a glass rod placed in air has a refractive index of $1.5$ and a length of $45 \text{ cm}$ . One end of the rod is shaped as a convex surface with radius of curvature ${ R }_{ 1 }=10 \text{ cm}$ . Suppose we would like to use it to make our very own telescope from this glass rod, how should the other end be shaped? Be as precise as possible in your answer.

Details and Assumptions :

For those who are unaware of the working principle of the telescope, it will allow a far away or distant object along the principle axis to have its image formed within the telescope system.
The answer computed should be rounded to the nearest integer.

Concave curvature of radius

3 \text{ cm}

Convex curvature of radius

10 \text{ cm}

Convex curvature of radius

20 \text{ cm}

Concave curvature of radius

10 \text{ cm}

Concave curvature of radius

8 \text{ cm}

Convex curvature of radius

3 \text{ cm}

Convex curvature of radius

8 \text{ cm}

Concave curvature of radius

5 \text{ cm}

1 solution

Michael Mendrin
Aug 20, 2015

This problem is based on using two plano-convex lens back to back, in which case the focal length for the 10 cm radius lens is 20 cm, and for the 5 cm radius lens is 10 cm. Presumably, those two are combined, along with the distances from the "midplane" of the lens to the curved ends, adding another 10 cm and 5 cm for a total of 45 cm. But this is a SOLID glass rod, so the correct answer really should be convex 20 cm, which is not offered as a choice. See further details in the report section.

Going beyond the telescope

1 solution

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