Question

An image of the moon is focused onto a screen using a converging lens of focal length f= 36.3 cm. The diameter of the moon is 3.48×106 m, and its mean distance from the earth is 3.85×108 m. What is the diameter of the moon's image?

Answer 1

Can you find the distance of the image of the moon form the lens ?

Answer 2

I have tried this so many times i am honestly confused as where to start now

Answer 3

You start calculating the distance of the image of the moon form the lens. Use \[\frac{1}{Focal \ length} = \frac{1}{Object\ distance} + \frac{1}{Image\ distance}\] and then calculate magnification using \[m = -\frac{Image\ distance}{Object\ distance}\]

Answer 4

But magnification is also given by \[m = \frac{size \ of \ image}{size\ of\ object}\]

Answer 5

so 1/.363m -1/3.85E8

Answer 6

Correct

Answer 7

=-3.85E-8

Answer 8

then take that and divide by 3.85E8?

Answer 9

You should get: image distance = 36.3 cm (focal length)

Answer 10

This is because you can treat the object at a very large distance such that 1/ 3.85E8 = 0 compared to 1/.363 !

Answer 11

I am confused
so the answer is 1/.363?

Answer 12

Invert it to get image distance. See the formula again.
\[\frac{1}{0.363} = 0+ \frac{1}{Image\ distance}\]

Answer 13

image distance is equal to .363

Answer 14

so how do I find the diameter?

Answer 15

Find the magnification using the formula I mentioned above.

Answer 16

Oh my gosh thatnk you!