Angle of view
One of the best ways to see how different lenses gives different angles of view is to head over to Nikons homepage and spend 2 minutes with their lens simulator. You can find the link right here (credit: Nikon).
Lenses comes with a focal length expressed in millimeters. A very wide lens that takes in a lot of the scene (e.g. 150 degrees) is typically very short, say 12mm. A long lens that takes in a very small part of the scene is much longer, say 500mm. The benefits of a long lens is that you can get your subject really close in the frame despite it being far away in the real world, so naturally bird and wildlife photographers love long lenses as they can observe and photograph wildlife from afar. But the down side is a bit like a horse with blinders: you can’t really see all that much to the left and right – only straight ahead!
There is a direct correlation between the lens focal length and the angle of view: longer lenses yields more narrow angle of view. Actually, the angle of view with a long lens can be just a few degrees, and you will notice this when you try to hold a camera with a long lens in your hands: you really have to hold the lens still in order not to make you feel seasick! The slightest movement of the lens will make what you see in the viewfinder jump a lot! So wildlife photographers often have their long lenses on a tripod, not only because the lens is heavy, but also because there is a strong incentive to hold the lens still!
Now, instead of being bugged down by all this, I suggest you head over to Nikons lens simulator. You can find the link right here (credit: Nikon).
Here you can select a lens and a camera body, and see how it works on a given scene. In the example below, I have chosen a zoom lens that ranges from 24-70 mm and gone all the way to 24mm by pulling the slider all the way to the left. In the middle of the slider, the yellow part of the half circle shows that the angle of view here is approximately 84 degrees.
When I pull the slider all the way to the right, the simulator shows what happens at 70mm: the angle of view is now reduced to 34 degrees (notice how much more narrow the yellow part of the half circle is). And the lighthouse has now moved much closer.
If you look carefully, you will see that the bright part of the beach just to the right of the dark stones, is gone when zoomed in. This is a consequence of using a longer focal length: the angle of view is narrowed and parts of what used to be visible in the edges of the frame is now cut away when zooming in.
Some say that it would be much more useful if we instead of talking about lenses in terms of their focal lengths, rather talked about their angle of view. But it has become a standard now, so I guess we have to live accept it. And as if this was not sufficient confusion, hear this: the size of the sensor changes the focal length of the lens! A lens that on a full frame camera is 50mm is on a cropped sensor (APS-C) the equivalent of a 75mm lens. You can also test this in the lens simulator from Nikon.