Producing images with telescopes

[element41$]

Homework Statement

A telescope has a mirror with a focal length of +3 meters and the distance from the mirror the the eyepiece is 3.5 meter. If the eyepiece is 3.5 meter.

a. If the eye piece has a focal length of 50 cm, where would the image produced by the eyepiece be? Could the image be projected on a screen at that location?

b. this is the case for astronomical telescopes, so how do you get an image when you look in the eyepiece? {hint: If you use a digital camera with no lens, you must reposition the eyepiece with the focus knob.}

Homework Equations

n/a

The Attempt at a Solution

this is what i got:

a. The image would be produced at the eyepieces focal length. so 0.5m from the eyepiece. Yes this image could be projected on a screen at this location.

b.With astronomical telescopes we can see a image while looking into the eyepiece because we can adjust the eyepieces focal length until it is clear to our eyes.


Thank you

 

[anathema]

for your response. Your understanding of the focal length and image formation is correct. However, there are a few additional points to consider:

a. Yes, the image would be produced at the eyepiece's focal length, which is 0.5 meters. However, in order for the image to be projected onto a screen, the screen would need to be placed at the focal point of the eyepiece, which is 0.5 meters away from the eyepiece. So the image would actually be projected 0.5 meters away from the eyepiece, not at the eyepiece itself.

b. In an astronomical telescope, the eyepiece is used to magnify the image formed by the primary mirror or lens. The focus knob adjusts the distance between the eyepiece and the primary mirror or lens, allowing the image to be brought into focus. This is similar to how a digital camera works - by adjusting the distance between the lens and the image sensor, the image can be brought into focus. So in both cases, the image is formed by the primary element (mirror or lens) and then magnified by the eyepiece or lens.