Is My Book Wrong? Explaining Lens in Interference & Diffraction

[kahwawashay1]

My book says that "One property of a converging lens is that it focuses all rays that are parallel to one another to the same point on its focal plane". But isn't that wrong? I mean, don't the rays have to be parallel to the central axis through the lens, not just to one another?

In any case, my book is describing a situation where you have a convex lens between a double slit and screen, with the screen exactly focal length from lens, and light being shined through the slits. My book says that in this case, all of the rays that end up on the screen had to have been initially "parallel"..im assuming they mean parallel to central axis, but they don't say to what..but then I think they want to justify in the derivation of the interefence formulas the assumption made about the rays ending up at any point on the screen being parallel to each other...but I don't understand why all of the rays on the screen must have had initially been parallel...not all of the rays entering the slit are parallel to each other or to the central axis, and so they all hit the lens in different ways, and so some end up at the focal point and some dont, but they all end up on the screen, regardless if they were initially parallel or not..

I understand how interference and diffraction with single and multiple slits works, but I don't understand at all what my book is trying to say about the lens in the middle..Could someone please explain the significance of the situation? Is it somehow different from when you just have the slits and screen?

 

[Khashishi]

You are right. Parallel rays that aren't parallel to the optical axis won't be sent to the same point on the focal plane. I don't know anything about the significance of the example though.

 

[cmos]

My book says that "One property of a converging lens is that it focuses all rays that are parallel to one another to the same point on its focal plane". But isn't that wrong? I mean, don't the rays have to be parallel to the central axis through the lens, not just to one another?

The book is correct.

If the rays are parallel to each other, but subtend an angle with the optical axis (i.e., the "central axis through the lens"), then the rays will come to a focus on the focal plane but NOT on the optical axis. The focal plane is the plane normal to the optical axis that contains the focal point.

Hopefully the attached figure makes sense.

 

[K^2]

What cmos said is absolutely correct. Do keep in mind that all of this is thin lens approximation to geometrical optics, however. So if it feels a little unnatural, it is because it is a simplification. Real optics is far more complex, but what you get from these assumptions is still very useful.

 

[kahwawashay1]

The book is correct.

If the rays are parallel to each other, but subtend an angle with the optical axis (i.e., the "central axis through the lens"), then the rays will come to a focus on the focal plane but NOT on the optical axis. The focal plane is the plane normal to the optical axis that contains the focal point.

Hopefully the attached figure makes sense.

You guys are not reading my initial message right.

I understand that all of the rays end up on the focal PLANE. But my book says that "all rays that are parallel to one another" converge "to the same POINT on its focal plane"

 

[AlephZero]

All the rays that are parallel in one particular direction converge to a point in the focal plane.

All the rays that are parallel but in a different direction converge to a different point in the focal plane.

The image that cmos posted shows what this means. The parallel rays do not have to be parallel to the axis of the lens.

If English is not your first language, this use of "the same point" might be confusing you. It means "one point for each set of parallel rays", not "one point for every set of parallel rays".

 

[sophiecentaur]

It is often easier to assume the book is wrong, rather than questioning ourselves as to whether we are reading it correctly.

"Dogs must be carried on the travellator." Does this imply that everyone must carry a dog?

 

[kahwawashay1]

If English is not your first language, this use of "the same point" might be confusing you. It means "one point for each set of parallel rays", not "one point for every set of parallel rays".

Ohhhhh thank you I get it now!