An old refracting telescope in a museum is 44.0 cm long and the caption states that the telescope magnifies images by a factor of 29.0. Assuming these numbers are for viewing an object an infinite distance away with minimum eyestrain, what is the focal length of each of the two lenses?
cm (objective)
cm (eyepiece)
For this I have done fo/fe = 29 and fo+fe = 44
29fe = 44
fe=1.6
then
(29)(1.6) = 46.4
But both these answers are wrong. Why? I cannot figure this out for the life of me. Please help.
if fo/fe = 29 and fo+fe = 44
then
fo=29fe
fo+fe=29fe+fe=30fe=44
fe=1.47
fo=44-fe=42.53
Actually, those answers are incorrect.
To find the focal length of each lens in the refracting telescope, we can use the lens formula:
1/f = 1/fo + 1/fe
Where f is the focal length of the telescope, fo is the focal length of the objective lens, and fe is the focal length of the eyepiece lens.
Given that the telescope magnifies images by a factor of 29, we know that fo/fe = 29.
We are also given that the total length of the telescope is 44.0 cm, which means:
fo + fe = 44.0
Now we can solve these equations simultaneously to find the focal lengths.
First, let's solve for the focal length of the eyepiece lens:
From the equation fo/fe = 29, we can rearrange it to fe = fo/29.
Substituting this into the equation fo + fe = 44, we get:
fo + fo/29 = 44
Multiplying through by 29 to eliminate the denominator, we have:
29fo + fo = 44 * 29
Combining like terms, we get:
30fo = 44 * 29
Dividing both sides by 30 to isolate fo, we have:
fo = (44 * 29) / 30
Evaluating this, fo ≈ 42.9333 cm
Next, we can find the focal length of the eyepiece lens (fe) by substituting the value of fo into the equation fo + fe = 44:
42.9333 + fe = 44
Subtracting 42.9333 from both sides, we get:
fe = 44 - 42.9333
Simplifying, fe ≈ 1.0667 cm
Therefore, the focal length of the objective lens (fo) is approximately 42.9333 cm, and the focal length of the eyepiece lens (fe) is approximately 1.0667 cm.
It seems that the mistake you made was in the calculations. Double-check your arithmetic and make sure you're using the correct units.