Does Convex Mirror Thickness Affect Focal Length and Image Sharpness?

[heavystray]

hello guys, so i want to ask whether the thickness of a convex/concave mirror affect its focal length and the sharpness of image formed? and what really determines the sharpness of image? thanks for replying in advance!

 

[blue_leaf77]

whether the thickness of a convex/concave mirror affect its focal length and the sharpness of image formed?

Definitely, it does.
EDIT: It depends on which thickness you meant.

what really determines the sharpness of image?

Aberrations and the so-called Abbe diffraction limit are widely known as the main sources of image quality degradation upon imaging process.

 

[heavystray]

Definitely, it does.

Aberrations and the so-called Abbe diffraction limit are widely known as the main sources of image quality degradation upon imaging process.

thank you so so much for replying.
again from the 1st question, what is the relationship between the thickness of a curved mirror and its focal length? does it follow the same principle like lenses? thick lenses, short focal length and vice versa
and also i have read it somewhere, thin convex mirror will produce a better quality of image, if so, why?

2. i do not quite understand why lenses with more curvature have short focal length. curvature means the degree at which something is curved right, so if you think logically, when the curvature of lenses increases, the radius of curvature will be increased too?
3. does thick lenses have more curvature and vice versa
4. why does a mirror with small aperture produce a sharper image

 

[nasu]

What do you mean by the thickness of a mirror? A mirror is just a reflecting surface. You mean the thickness of the reflecting (usually metallic) layer used to produce a mirror?

 

[heavystray]

What do you mean by the thickness of a mirror? A mirror is just a reflecting surface. You mean the thickness of the reflecting (usually metallic) layer used to produce a mirror?

yes. that's why i ask whether it affects the focal length and the quality of image

 

[blue_leaf77]

Ah my bad, I mistook your problem as that with lenses. No, if the reflecting surface is the surface of the mirror itself and no penetration is possible, its thickness won't matter to the reflected wave. Note: up to now I'm assuming your definition of mirror thickness as the distance between the mirror's vertex and its back.

also i have read it somewhere, thin convex mirror will produce a better quality of image, if so, why?

I think you should recheck again how this source defines the thickness of a mirror.

2. i do not quite understand why lenses with more curvature have short focal length. curvature means the degree at which something is curved right, so if you think logically, when the curvature of lenses increases, the radius of curvature will be increased too?

"We will see that the radius of curvature, which is a length is exactly the reciprocal of the curvature", quoted from http://ocw.mit.edu/ans7870/18/18.013a/textbook/HTML/chapter15/section03.html

3. does thick lenses have more curvature and vice versa

The curvature of a lens is something you can control during the fabrication, you can have thick lenses with small or big curvature.

4. why does a mirror with small aperture produce a sharper image

May be you meant depth of field instead of sharpness. If you really mean sharpness, it's the other way around, restricting the aperture to small diameter will reduce the image's resolution.

 

[nasu]

It may affect the quality of the image if the layer is so thin that a significant amount of light goes through rather than being reflected.

 

[heavystray]

Ah my bad, I mistook your problem as that with lenses. No, if the reflecting surface is the surface of the mirror itself and no penetration is possible, its thickness won't matter to the reflected wave. Note: up to now I'm assuming your definition of mirror thickness as the distance between the mirror's vertex and its back.

I think you should recheck again how this source defines the thickness of a mirror.

"We will see that the radius of curvature, which is a length is exactly the reciprocal of the curvature", quoted from http://ocw.mit.edu/ans7870/18/18.013a/textbook/HTML/chapter15/section03.html

The curvature of a lens is something you can control during the fabrication, you can have thick lenses with small or big curvature.

May be you meant depth of field instead of sharpness. If you really mean sharpness, it's the other way around, restricting the aperture to small diameter will reduce the image's resolution.

ok thanks for the help, i will ask my teacher about the thin convex mirror

 

[heavystray]

It may affect the quality of the image if the layer is so thin that a significant amount of light goes through rather than being reflected.

oh really? you're saying than some of the light may get refracted?

 

[Merlin3189]

4. why does a mirror with small aperture produce a sharper image

Might it depend on the shape of the mirror?
I expect now someone has worked out a shape which has a flat focal plane, but when I learned about mirrors at school, they were either spherical or parabolic and neither had a flat focal plane. Provided their aperture was small enough compared to their focal length, the approximation was good enough. Hence, smaller = sharper down to reasonable size.

Since every advert I see these days for lenses says, "diffraction limited optics", I assume people have now calculated shapes which avoid all the other aberrations we were taught about?

 

[heavystray]

Might it depend on the shape of the mirror?
I expect now someone has worked out a shape which has a flat focal plane, but when I learned about mirrors at school, they were either spherical or parabolic and neither had a flat focal plane. Provided their aperture was small enough compared to their focal length, the approximation was good enough. Hence, smaller = sharper down to reasonable size.

Since every advert I see these days for lenses says, "diffraction limited optics", I assume people have now calculated shapes which avoid all the other aberrations we were taught about?

i can't understand what you're trying to say, sorry. i haven't learned about aberrations. thanks of replying anyway

 

[Merlin3189]

Sorry to cause confusion. I suppose my remark was addressed more to the other responders, asking them whether this might be an explanation for your Q4.

Aberration simply means faults in the image produced by a lens or mirror.

For example, with a spherical concave mirror, with rays parallel to the axis, the rays close to the axis are focussed further away from the mirror than rays striking the edge of the mirror. So you get a blurred image. The wider the mirror is, the worse this effect, so a smaller aperture mirror may give a sharper image because more of the light is closer to the axis.

However, my original comment may be wrong, in that parabolic mirrors do not show this "spherical" aberration. I thought they did show other faults, but have been unable to find any reference for that. Spherical mirrors are still used, because they are easier to manufacture than parabolic mirrors.

 

[heavystray]

Sorry to cause confusion. I suppose my remark was addressed more to the other responders, asking them whether this might be an explanation for your Q4.

Aberration simply means faults in the image produced by a lens or mirror.

For example, with a spherical concave mirror, with rays parallel to the axis, the rays close to the axis are focussed further away from the mirror than rays striking the edge of the mirror. So you get a blurred image. The wider the mirror is, the worse this effect, so a smaller aperture mirror may give a sharper image because more of the light is closer to the axis.

However, my original comment may be wrong, in that parabolic mirrors do not show this "spherical" aberration. I thought they did show other faults, but have been unable to find any reference for that. Spherical mirrors are still used, because they are easier to manufacture than parabolic mirrors.

so, just to check my understanding, if you have a wider aperture mirror, the difference between the ray close to axis and ray at the edge will be further right? so you get more blurred image? am i right?

 

[Drakkith]

Aberrations are enhanced when the focal ratio of the mirror or lens is low vs when it is high. A smaller diameter spherical mirror has less spherical aberration only if the focal length is the same as the larger diameter mirror. An f/4 spherical mirror has the same amount of spherical aberration regardless of its diameter.

The same concept applies to effectively all types of aberrations. Large, short focal length mirrors and lenses give you excellent light gathering and a wide field of view, but are very expensive to use since you need to correct all those aberrations.

 

[blue_leaf77]

if you have a wider aperture mirror, the difference between the ray close to axis and ray at the edge will be further right? so you get more blurred image? am i right?

I was only considering perfect mirror in post #6 where the image resolution is diffraction limited, and hence should get worse when the aperture size is reduced. But in the presence of aberration, you are right, smaller aperture will block rays which would have had bigger focus offset and hence suppressing image blurring.
In short, there is an interplay when increasing/decreasing aperture. Increase aperture, more higher (spatial) frequency components can be collected but you get more aberration effect. Decrease aperture, less collected higher frequency component but suppressed aberration. In addition to all these, there is also the depth of field which is altered by the changing of the aperture. More precisely, larger aperture decreases depth of field - good for taking close up pictures where you want to accentuate the main object while blurring the background.

 

[heavystray]

v

Aberrations are enhanced when the focal ratio of the mirror or lens is low vs when it is high. A smaller diameter spherical mirror has less spherical aberration only if the focal length is the same as the larger diameter mirror. An f/4 spherical mirror has the same amount of spherical aberration regardless of its diameter.

The same concept applies to effectively all types of aberrations. Large, short focal length mirrors and lenses give you excellent light gathering and a wide field of view, but are very expensive to use since you need to correct all those aberrations.

Aberrations are enhanced when the focal ratio of the mirror or lens is low vs when it is high. A smaller diameter spherical mirror has less spherical aberration only if the focal length is the same as the larger diameter mirror. An f/4 spherical mirror has the same amount of spherical aberration regardless of its diameter.

The same concept applies to effectively all types of aberrations. Large, short focal length mirrors and lenses give you excellent light gathering and a wide field of view, but are very expensive to use since you need to correct all those aberrations.

understood. thank you!

 

[heavystray]

I was only considering perfect mirror in post #6 where the image resolution is diffraction limited, and hence should get worse when the aperture size is reduced. But in the presence of aberration, you are right, smaller aperture will block rays which would have had bigger focus offset and hence suppressing image blurring.
In short, there is an interplay when increasing/decreasing aperture. Increase aperture, more higher (spatial) frequency components can be collected but you get more aberration effect. Decrease aperture, less collected higher frequency component but suppressed aberration. In addition to all these, there is also the depth of field which is altered by the changing of the aperture. More precisely, larger aperture decreases depth of field - good for taking close up pictures where you want to accentuate the main object while blurring the background.

understood, thank you very much