Question
Do zoom lenses typically have worse geometric distortion compared to fixed-focal-length lenses? Is the difference significant?
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Zoom lenses have variable focal lengths, allowing for a range of magnifications, while fixed-focal-length lenses (also known as prime lenses) have a single, unchangeable focal length. Show more…
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Your camera may have a zoom lens, ranging between wide angle (short focal length) and telephoto (long focal length). How does the size of an object in the camera's focal plane differ between wide angle and telephoto?
. Zoom lens, I. A zoom lens is a lens that varies in focal length. The zoom lens on a certain digital camera varies in focal length from 6.50 $\mathrm{mm}$ to 19.5 $\mathrm{mm}$ . This camera is focused on an object 2.00 $\mathrm{m}$ tall that is 1.50 $\mathrm{m}$ from the camera. Find the distance between the lens and the photo sensors and the height of the image (a) when the zoom is set to 6.50 $\mathrm{mm}$ focal length and (b) when it is at 19.5 $\mathrm{mm}$ . (c) Which is the telephoto focal length, 6.50 $\mathrm{mm}$ or 19.5 $\mathrm{mm} ?$
Focal Length of a Zoom Lens. Figure $\mathbf{P 3 4 . 9 9}$ shows a simple version of a zoom lens. The converging lens has focal length $f_{1}$ and the diverging lens has focal length $f_{2}=-\left|f_{2}\right| .$ The two lenses are separated by a variable distance $d$ that is always less than $f_{1}$. Also, the magnitude of the focal length of the diverging lens satisfies the inequality $\left|f_{2}\right|>\left(f_{1}-d\right) .$ To determine the effective focal length of the combination lens, consider a bundle of parallel rays of radius $r_{0}$ entering the converging lens. (a) Show that the radius of the ray bundle decreases to $r_{0}^{\prime}=r_{0}\left(f_{1}-d\right) / f_{1}$ at the point that it enters the diverging lens. (b) Show that the final image $I^{\prime}$ is formed a distance $s_{2}^{\prime}=\left|f_{2}\right|\left(f_{1}-d\right) /\left(\left|f_{2}\right|-f_{1}+d\right)$ to the right of the diverging lens. (c) If the rays that emerge from the diverging lens and reach the final image point are extended backward to the left of the diverging lens, they will eventually expand to the original radius $r_{0}$ at some point $Q .$ The distance from the final image $I^{\prime}$ to the point $Q$ is the effective focal length $f$ of the lens combination; if the combination were replaced by a single lens of focal length $f$ placed at $Q$, parallel rays would still be brought to a focus at $I^{\prime} .$ Show that the effective focal length is given by $f=f_{1}\left|f_{2}\right| /\left(\left|f_{2}\right|-f_{1}+d\right) .(\mathrm{d})$ If $f_{1}=12.0 \mathrm{~cm}, f_{2}=-18.0 \mathrm{~cm},$ and the separation $d$ is adjustable between 0 and $4.0 \mathrm{~cm}$, find the maximum and minimum focal lengths of the combination. What value of $d$ gives $f=30.0 \mathrm{~cm} ?$
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