Not really a math question, more physics, but I'm lost so if someone here could help me out I'd really appreciate it, it's 00:40 and I'm panicking because I don't understand them oof! It's about the lensformula.
a. An arrow of 2cm length stands about 6cm away from a convex lens (f = 2cm). How long is the image of the arrow?
[ ] A 1 cm [ ] D 4 cm
[ ] B 2 cm [ ] E 6 cm
[ ] C 3 cm
b. A windmill on an lcd-screen of a beamer is 3 cm high. On the projectionscreen the windmill is 90 cm high. The lens has a strength of 10 dpt.
What's the distance from the lens to the lcd-screen
[ ] A 0,103 cm [ ] C 10,0 cm
[ ] B 5,15 cm [ ] D 10,3 cm
+776 a)
Height of arrow = 2cm
Distance from lense = 6cm
Focal length = 2cm
Formula: 1/f = 1/v +1/u Note: f = focal length, v = image of arrow's distance from lens, u = object's distance from lens
notice that the values are inverted because they are on the opposite side of the lens (opposite side of the arrow)
-1/2 = -1/6 +1/v
1/v = -1/2 + 1/6, which simplifies into 1/v = -1/3
v = -3 cm
This means that the height of the image is upside down, but it is still 3 cm.
(If you know physics, the virtual image behind the convex lens turns upside down if the object is behind the focal point of the convex lens.)
Height of image/Height of object = -v /u = 3/6 = 1/2
Height of image / 2 = 1/2 Note: height of image (virtual reflection) of arrow = h
Multiply by 2 on both sides to get \(\boxed{h = 1cm}\).
The answer to a) is \(\boxed{A}\).
Hope this helps,
- Partial Physician (Partial Mathematician)
+776 For b), try to follow along with what I did in a). Use the variable "v" to represent the "virtual image's distance from the convex lens".
I'll give you the starting variables.
Height of windmill = 3cm = height of object
Height of virtual image = 90 cm = h
Lens strength = 10 dpt = focal length 10 cm
- Partial Physician/Mathematician
Thanks for the reply!
Height of windmill = 3cm = height of object
Height of virtual image = 90 cm = h
Lens strength = 10 dpt = focal length 10 cm
Formula: 1/f = 1/v +1/u
1/10 = 1/3 + 1/u
1/u = 1/f - 1/u
1/u = 1/10 - 1/3
1/u = -0,2333 or - 7/30
-v /u = - 7/30 / 1/3 = -0,1
so it'd be C then?
