# Building a Telescope: Calculating Total Magnification & Length

• frostking
In summary, the total possible magnification for the telescope is 10X. The 2X lens should be used as the objective due to its longer focal length and smaller magnification. The formula for magnification (M = 25/F) is not necessary for a telescope and the magnification is instead determined by the ratio of the two focal lengths. The specifications of the magnifying lenses are needed to find this ratio. The length of the telescope is 55 cm.
frostking

## Homework Statement

I need to build a telescope from two magnifying lens, one is 2x the other is 5x. First I need to give the total magnification possible, state which lens to use as the objective and finally to state the length of the telescope.

## Homework Equations

l Ml = Fo/Fe total magnification is lM1l x lM2l Length = Focal length of objective + focal length of eyepiece

## The Attempt at a Solution

The total possible magnification is 10X. I use the 2X for the objective because you need a long focal length and smaller magnification. I am stuck on how to get the length of the scope. I know the absolute value of M and can say that Fobjective is equal to lMl times F of eyepiece. But I don't have either focal length as far as I can tell and so I have no way to determine the length. I have the answer, so I know it should be 55 cm but why? Any help would be much appreciated. Frostking

There's a formula that relates the magnification of a magnifying glass with its focal length. Do you know what it is?

Yes, silly me it is M = 25/F On exams we are only allowed to use formulas on our formula sheet or that can be derived from the formula sheet. This formula is NOT provided. I guess I will just have to memorize this and hope that it is allowed to be used on the final. Thanks and sorry for wasting your time. Frostking

This formula is valid for magnifying glass. You don't need it for telescope.
For a telescope the magnification is given by the ratio of the two focal lengths.

nasu said:
This formula is valid for magnifying glass. You don't need it for telescope.
For a telescope the magnification is given by the ratio of the two focal lengths.

Thanks so much. I will remember this and use it! Frostking

You don't need the formula for a telescope, but the specifications of the magnifying glasses are given. I can't see how you would find the ratio of the focal lengths without using these specifications.

## 1. How do I calculate the total magnification of a telescope?

The total magnification of a telescope is calculated by multiplying the magnifying power of the eyepiece by the magnifying power of the objective lens. For example, if the eyepiece has a magnifying power of 10x and the objective lens has a magnifying power of 30x, the total magnification of the telescope would be 300x.

## 2. How do I determine the focal length of a telescope?

The focal length of a telescope can be determined by measuring the distance between the objective lens and the point at which the image is in focus. This distance is typically marked on the telescope's body and can also be calculated by dividing the focal length of the eyepiece by the telescope's magnifying power.

## 3. What is the formula for calculating the magnifying power of an eyepiece?

The formula for calculating the magnifying power of an eyepiece is MP = FL(eyepiece)/FL(objective lens), where MP represents magnifying power, FL represents focal length, and the subscripts indicate the specific lens.

## 4. How do I choose the right eyepiece for my telescope?

The right eyepiece for your telescope depends on the desired magnification and the focal length of your telescope. A shorter focal length eyepiece will provide higher magnification, while a longer focal length will provide a wider field of view. It is recommended to have a variety of eyepieces with different focal lengths to have a range of magnifications available.

## 5. Can I change the magnifying power of my telescope?

Yes, the magnifying power of a telescope can be changed by switching out the eyepiece with one of a different focal length. However, the maximum magnification of a telescope is limited by the diameter of the objective lens. To avoid image distortion and loss of clarity, it is recommended to not exceed a magnification of 2x the diameter of the objective lens in millimeters.

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