To imagine the 50mm focal length of a prime lens 1.4F, can I simply zoom the lens of my point and shoot camera up to 50mm?
Will both the focal lengths be same?
Any other way to imagine the focal length 50mm of prime lens 1.4F when what you only have is a point and shoot camera with 70mm max zoom?
If your point-and-shoot has the typical 1/2.3" format sensor and you are trying to compare it to a 50mm lens on a cropped-sensor DSLR (in your case, a Nikon, if I recall correctly), then there's a little bit of math involved.
The compact's sensor has a 3:4 aspect ratio. It measures 6.16mm by 4.62mm, with a diagonal of 7.70mm.
The Nikon DX sensor has an aspect ratio of 2:3 and measures 23.6mm by 15.8mm. That would give a diagonal of 28.4mm.
It's normal to compare lenses based on the diagonal of the negative/sensor. I don't like that approach, though, since the aspect ratio is different. It's best to compare images with the same aspect ratio, and in the case of both of these sensor formats, the full length of the short side of the sensor will be used when an image is printed in a 4:5 aspect ratio. That is, an 8x10 picture made with either camera would involve cropping the longer dimension. So it's safe to compare just the shorter dimension of each camera/lens combination.
The 50mm lens on the Nikon is about 3.165 times the length of the shorter side (the height when the camera is held horizontally). That means that in order to get the "same" 8X10 from your compact camera, the lens would have to be set to 3.165 times the shorter side of its sensor, or about 14.6mm.
If your compact has a different-sized sensor, the math will still hold. Find out what format of sensor it uses, then multiply the shorter side of the sensor by 3.165 to find out how far out the lens needs to be zoomed to approximate the 50mm lens. Do note, though, that the field of view for our hypothetical 8X10 print is the only thing the two cameras will have in common.
Or, if you want to do it without the math, my rather standard 8-1/2" (about 21.5cm) tall head will completely, but just, fill the frame of a Nikon DX in "landscape" orientation from the top of my bald pate to the bottom of my chin using a 50mm lens from almost exactly three feet away. So a volunteer or a ruler three feet (90cm) away or a mirror 18 inches (45cm) away will be enough to show you how far to zoom.
The answer here is made more complicated by the fact that your point and shoot is almost certainly lying to you. If you have, for example, a Canon Powershot SX210, the focal length range is actually 5mm to 70mm, but many point and shoot cameras — especially in their specifications — translate that to the focal length of a 35mm film camera which would give the same field of view. That means the lens in the SX210 example is quoted as having a 28mm to 392mm zoom range. (That's because the diagonal measurement of the sensor is 5.6 times smaller than that of 35mm film or "full frame".)
Stan is right (in his answer) that since the frame is a different shape, using the diagonal is a bit misleading, but it's rather close — and see my last paragraph on that.
Meanwhile, lenses for APS-C are given with their real focal length, which means that a 50mm lens for a Nikon DSLR is just what it says, but taking into account the smaller sensor produces images with the field of view equivalent to a 75mm lens on a full-frame camera.
So, to put those two things together: assuming your camera has a sensor the same size as the SX210, you'll want to set the focal length to around 13.4mm — which the camera may call "75mm". (It'll be several zoom steps in, in any case.) That will give you the same field of view you'll get with a 50mm prime on a Nikon, Sony, or Pentax entry- or mid-level DSLR.
Most point and shoot cameras use a stepper motor for zoom. You can't pick an arbitrary focal length; there are pre-set steps. For some reason this is rarely mentioned in reviews, but the fact is you're only going to be able to get close to some arbitrarily precise equivalent. That means you can use this idea to get a rough impression of the focal length, but worrying too much about getting it exact will be a waste of energy.
You are probably not trying to compare the focal lengths (that is pointless, 50mm is always 50mm, no matter what camera you use), but the field of view that will result in using this focal lenght. The field of view is dependent no only of the focal lenght but also the size of sensor used. So you will need to know the size of the sensor in your compact camera and the camera you would be using the 50mm prime lens on. You can see the sensor sizes for example from http://www.dpreview.com (under Database). For example lets assume that your compact camera has a sensor width of 6mm and the DSLR you will use the prime on has a sensor width of 24mm. 24 / 6 = 4. This means that your compact camera has a sensor that is 4 times smaller and thus also the field of view is 4 times narrower for the same focal length. To see the field of view of the 50mm prime on a DSLR with aforementioned sensor width you would need to set your compact camera to use focal length 50 / 4 = 12.5 mm. A calculator is also available on this web page, scroll down to the "Lens Equivalence / Diffraction Calculator". You can ignore the aperture value. The linked calculator also has the advantage of using the sensor diagonal instead of my simplified calculation with only the sensor width.
