lenses and focal points?

[altogether]

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So I'm reading EK physics and they says for a converging lens the focal point is on the side opposite the object and for a diverging lens, the focal point is on the same side as the object. However in all my other books it is the opposite.

Can anyone explain what they are trying to do there?

 

[tartrate]

Lenses have two focal points, one on each side.

From wiki:

For a lens, or a spherical or parabolic mirror, it is a point onto which collimated light parallel to the axis is focused. Since light can pass through a lens in either direction, a lens has two focal points—one on each side.

For practical purposes of understanding, consider where parallel light rays would focus on in respect to the viewer. This will give you a working focal point to solve problems with.

 

[phltz]

The focal points for a converging and diverging lenses are slightly different beasts.

If parallel rays of light (as from an extremely distant object) come into a converging lens along the axis of symmetry, after passing through the lens the rays will converge, and all come together at the focal point. They will converge at the focal point which is on the opposite side of the lens from the original object.

In parallel rays of light (as from an extremely distant object) come into a diverging lens along the axis of symmetry, after passing through the lens the rays will diverge, and fan out away from each other. They will thus never all come together at one point. However, if you were to trace their trajectories backwards, they would appear to have originated at the focal point on the same side on the lens as the object.

For a converging lens, the light actually converges at the focal point on the opposite side of the lens from a distant object. For a diverging lens, the light seems to have originated from the focal point on the same side of the lens as a distant object. These focal points are thus similar in many ways, but also crucially different. This is part of the reason that we sometimes treat the one focal length as positive, and the other as negative.

 

[FIREitUP]

Excellent explanation. But don't forget that when the object is within the focal point of a converging lens, the image appears to be on the same side of the object, is upright, larger, and imaginary.

The focal points for a converging and diverging lenses are slightly different beasts.

If parallel rays of light (as from an extremely distant object) come into a converging lens along the axis of symmetry, after passing through the lens the rays will converge, and all come together at the focal point. They will converge at the focal point which is on the opposite side of the lens from the original object.

In parallel rays of light (as from an extremely distant object) come into a diverging lens along the axis of symmetry, after passing through the lens the rays will diverge, and fan out away from each other. They will thus never all come together at one point. However, if you were to trace their trajectories backwards, they would appear to have originated at the focal point on the same side on the lens as the object.

For a converging lens, the light actually converges at the focal point on the opposite side of the lens from a distant object. For a diverging lens, the light seems to have originated from the focal point on the same side of the lens as a distant object. These focal points are thus similar in many ways, but also crucially different. This is part of the reason that we sometimes treat the one focal length as positive, and the other as negative.