- #1
arnoke
- 9
- 0
Hi all,
This is probably a silly questions, but I want to be sure :).
I'm wondering if a real image, created by a convex lens, can appear larger than the lens diameter itself.
As an example, I'm thinking about the following:
- I have a an object of height [itex]h_0=7.76"[/itex] (display size of my IPAD :p)
- Two convex fresnel lenses, each width diameter of [itex]8"[/itex] and focal length [itex]12.5"[/itex]
- The lenses will be put back-to-back, so the combined focal length is [itex]f=6.25"[/itex]
- I will place the IPAD at distance [itex]d_0=1.2f=7.5"[/itex] from the lens
Now I can calculate at which distance the real image will appear to float in front of the lens:
[itex]\frac{1}{f}=\frac{1}{d_0}+\frac{1}{d_1}[/itex]
[itex]\Rightarrow d_i = \frac{1}{1/f - 1/d_0} = \frac{1}{(1/6.25 - 1/7.5} = 37.5"[/itex]
Also I can calculate the magnification:
[itex]\frac{h_i}{h_0}=-\frac{d_i}{d_0}[/itex]
[itex]\Rightarrow h_i = -h_0\frac{d_i}{d_0} = -7.76\frac{37.5}{12.5} = -23.28"[/itex]
So the real object would be at [itex]37.5"[/itex] from the lens, inverted, and would be [itex]23.28"[/itex] high.
Now my question is; would I indeed see an IPAD of height [itex]23.28"[/itex] if my (fresnel) lens has the same size as the original Ipad? Or should my lens be at least of diameter [itex]23.28"[/itex], the same size as the magnified, real image?
Thanks a lot for your input!
This is probably a silly questions, but I want to be sure :).
I'm wondering if a real image, created by a convex lens, can appear larger than the lens diameter itself.
As an example, I'm thinking about the following:
- I have a an object of height [itex]h_0=7.76"[/itex] (display size of my IPAD :p)
- Two convex fresnel lenses, each width diameter of [itex]8"[/itex] and focal length [itex]12.5"[/itex]
- The lenses will be put back-to-back, so the combined focal length is [itex]f=6.25"[/itex]
- I will place the IPAD at distance [itex]d_0=1.2f=7.5"[/itex] from the lens
Now I can calculate at which distance the real image will appear to float in front of the lens:
[itex]\frac{1}{f}=\frac{1}{d_0}+\frac{1}{d_1}[/itex]
[itex]\Rightarrow d_i = \frac{1}{1/f - 1/d_0} = \frac{1}{(1/6.25 - 1/7.5} = 37.5"[/itex]
Also I can calculate the magnification:
[itex]\frac{h_i}{h_0}=-\frac{d_i}{d_0}[/itex]
[itex]\Rightarrow h_i = -h_0\frac{d_i}{d_0} = -7.76\frac{37.5}{12.5} = -23.28"[/itex]
So the real object would be at [itex]37.5"[/itex] from the lens, inverted, and would be [itex]23.28"[/itex] high.
Now my question is; would I indeed see an IPAD of height [itex]23.28"[/itex] if my (fresnel) lens has the same size as the original Ipad? Or should my lens be at least of diameter [itex]23.28"[/itex], the same size as the magnified, real image?
Thanks a lot for your input!