Final answer:
To build a 35-power telescope with an eyepiece focal length of 5.4 cm, the student needs an objective lens with a focal length of 189 cm. The objective lens focal length is calculated using the magnification formula for telescopes.
Step-by-step explanation:
The question pertains to the design of a telescope and is seeking to determine the focal length of the objective lens required to reach a specified magnification power. Based on the magnifying power (35-power) and the focal length of the eyepiece (5.4 cm), we can use the formula for the magnifying power of a telescope which is the focal length of the objective lens divided by the focal length of the eyepiece.
Setting up the equation: magnification = focal length of objective (fo) / focal length of eyepiece (fe). Therefore, fo = magnification × fe. Plugging in the values, we get fo = 35 × 5.4 cm, which gives us an objective lens focal length of 189 cm. To answer the student's question directly, the focal length needed for her objective lens is 189 cm in order to achieve the desired 35-power magnification for the telescope.