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I am currently considering buying either an Olympus OM-D EM-10 mark ii or a Nikon D3400. As a beginner I thought I would stick to the kit lenses for a while, and have seen that the specs of both kit lenses are quite similar (Zuiko 14-42mm f/3.5 -5.6 EZ vs NIKKOR 18–55 mm 1:3,5–5,6G VR).

However the size of the kit lens of the Olympus is just a fraction of the size of the nikon kit lens. So what are the (dis-)advantages to such a small lens? There must be a difference, otherwise everyone would simply build the smallest possible lens?

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There are several key differences here.

First, the Olympus lens needs to cover a smaller sensor — Micro Four Thirds uses a sensor which measures 17.3×13mm, while the Nikon DX camera uses a 23.5×15.6mm sensor. That means the Olympus lens needs to project an image circle with a diameter covering 21.6mm, while the Nikon lens needs to cover 28.2mm. That means everything in the Olympus lens can be correspondingly smaller.

(This sensor size difference is also why the Olympus lens has a shorter focal length, but approximately the same field of view.)

Additionally, the mirrorless design of the Olympus system allows flange focal distance ­— the distance from the lens mount to the sensor — to be smaller. That's about 19mm for Micro Four Thirds, and 46.5mm for Nikon.

Third, the Nikon lens features vibration reduction, while Olympus relies on that feature in the camera body.

I think both lenses basically are the "smallest possible lens", given the circumstances. However, it's also worth noting that larger-than-smallest-possible also can have ergonomic advantages: there's more room for focus and aperture rings, and those rings can have more travel.

There are also various other lens design choices which can influence the diameter — see more about that at How does the lens diameter influence photo quality? — but as a general rule there's nothing there that's going to be a big deal for a kit zoom.

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    \$\begingroup\$ Great answer thanks! So how noticeable is the difference in the image quality of the different sensor types? Does the smaller sensor necessarily mean a worse image? \$\endgroup\$ Commented Jan 10, 2018 at 18:55
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The OM-D is a Micro Four Thirds camera. As such, it's sensor is smaller than the Nikon's, it has a crop factor of 2 while the Nikon has a factor of 1.5.

A smaller sensor enables a smaller lens, just think of the miniscule lens of a smartphone.

The dis-/advantages don't lie so much in the lens, as in the differently sized sensors. Roughly, all else being equal, a smaller sensor will exhibit more noise, and have a deeper DoF at the same aperture.

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