Question

A 7.5× binocular produces an angular magnification of −7.50, acting like a telescope. (Mirrors are used to make the image upright.) If the binoculars have objective lenses with a 75.0 cm focal length, what is the focal length of the eyepiece lenses?

a) 10.0 cm
b) 5.0 cm
c) 15.0 cm
d) 20.0 cm

Answer 1

The focal length of the eyepiece lenses in 7.5x binoculars with an angular magnification of -7.50 and objective lenses of 75.0 cm focal length is 10.0 cm.

Step-by-step explanation:

The question pertains to determining the focal length of the eyepiece lenses in a set of 7.5x binoculars that provide an angular magnification of -7.50 and have objective lenses with a 75.0 cm focal length. In optics, the magnification (m) of a telescope-like system can be calculated using the equation m = -f_o / f_e, where f_o is the focal length of the objective lens and f_e is the focal length of the eyepiece lens. Given that the magnification is -7.50 and the objective lens's focal length is 75.0 cm, we can rearrange the equation to solve for the eyepiece lens's focal length: f_e = -f_o / m. Thus, the focal length of the eyepiece lenses is 10.0 cm.