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A typical zoom/telephoto lens can cost a lot but a Canon PowerShot SX40 model has a zoom lens of 24-840mm ! And the camera as a whole still costs less than a single lens.

I know that they differ a lot in sensor size, but what are the difference in the lens ? What are the tradeoffs in bridge cameras which allow for such a huge zoom range while still being cost effective ?

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It largely comes back to that tiny sensor -- the smaller the image circle it needs to produce, the easier it is to build a small, cheap lens to cover it (even with a wide zoom range). Even so, the lens is often of somewhat inferior quality. –  Jerry Coffin Aug 30 '12 at 5:08
    
Just don't entertain buying a bridge camera... I've never met one yet that produced images I liked. A high-end compact would even be better. –  Mike Aug 30 '12 at 7:51

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up vote 3 down vote accepted

The reason the lens in bridge cameras have massive zoom and still cheaper is because it is small compared to a DSLR lens.

The main reason behind this is the sensor size(i.e. crop factor)
The sensor size is a sensor of 6x crop factor. That implies that the image in the P&S sensor is cropped 6 times the image in Full frame sensor. This also can be said as the zoom in the P&S camera can be 6x at a given focal length compared to a Full frame camera.

The Specification 24-840 mm focal length of P&S is Full frame equivalent of the P&S lens.
So, the real focal length of the given P&S lens is 3-140 mm lens. Now you can anticipate how small really the 35x zoom on a P&S shoot compared to the DSLR lens.
This smaller focal length of lens can produce that much magnification in a P&S camera. This is the reason for the Cheap price.

Also P&S lens are not for professional purpose and hence there may be some compromise in quality to bring it to the cheaper price.

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Not to mention the aperture size doesn't get anywhere near wide enough to keep ISOs down in low light or (especially with the small sensor) separate background from foreground subjects. –  camflan Aug 30 '12 at 13:19
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Some compromise in quality is a massive understatement. Those compact cameras have a sensor that is 1/6 the size in both directions, so 1/36 the amount of light gathering capability, coupled with a resolution that's too high to match the resolvability of its lens. Low light shots will be a noisy, blurry, muddy mess in comparison to a DSLR. Even well lit shots won't be as sharp. –  thomasrutter Apr 26 '13 at 2:09

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