1.4 - angular resolution

why do close light sources appear like a singular light source?

the angles created from light rays entering your eye interfere with each other up, making the light source seem like a singular point

with the issue of close light sources appearing as a singular light source, is this prevalent in space? why?

its very common because in space, the distance between us and the stars is so large

what is it specifically about the 2 close light sources that makes it appear as a singular point source?

the angels of their rays

what is diffraction?

the spreading of waves around objects / through an aperture

what is an aperture?

a gap / opening

what are some examples of circular apertures?

• telescopes

• our eyes

what are circular apertures designed to do?

let light rays enter and let a singular ray of light act as a point source

what do circular apertures allow light rays to act as?

a singular ray of light acts as point source

in an aperture, how many rays act as a point source? eh

a singular ray

what is a point source?

rays of light coming from a singular source

why do rays from 2 close point sources appear as one when passing through a circular aperture?

because a circular aperture is designed to register rays as a single point source

how can we determine if rays of light are from a singular point source or from multiple light sources?

by passing them through a circular aperture, in which the rays diffract and create a circular diffraction pattern

DIAGRAM

how does diffraction vary with aperture size?

the smaller the aperture, the more diffraction

does diffraction increase or decrease with a smaller circular aperture?

the smaller the aperture, the more diffraction

does diffraction increase of decrease with a larger circular aperture?

the larger the aperture, the less diffraction

how does a circular aperture help determine the number of light sources rays come from?

DIAGRAM

the light rays diffract when passing through the circular aperture, creating a circular diffraction pattern

which kind of aperture do we use to diffract light rays?

a circular aperture

why do we use a circular aperture to diffract light rays?

because it produces a circular diffraction pattern, and this is good cuz…

what kind of diffraction pattern do diffracted light ways produce?

a circular diffraction pattern

why do light rays produce a circular diffraction pattern?

because the light rays pass through a circular aperture, making it diffract in a circular pattern

why is it beneficial for light rays to produce a circular diffraction pattern?

idk

what is a positive of diffraction?

because it separates the light rays and allows us to determine how many light sources there are

what is a negative of diffraction?

too much diffraction could make the image blurry because…

why does too much diffraction make an image blurry?

how much diffraction should take place?

enough for the outer ring of the circular diffractive patterns to just be overlapping. any less diffraction would not separate the light (eh), and any more would overlap the diffraction patterns, meaning we cannot resolve them and the image would be blurry

when we can resolve the diffraction patterns?

when their outer rings are just overlapping

when can’t we resolve the diffraction patterns?

• when they overlap any more than the outer rings

• when they don’t overlap at all

what is the minimum angular resolution?

• the quality of an image in regards to the minimum angle separation

• the smallest possible angle between point sources

what is minimum angular resolution the same as?

resolving power

what is resolving power the same as?

minimum angular resolution

what is resolving power?

• the quality of an image in regards to the minimum angle separation

• the ability of a lens to resolve two points which are close together

why do we consider the smallest angle in resolution?

because we’re considering 2 close light sources seeming as one point source, we consider how close 2 points can be and still be distinguishes

how does the magnitude of resolving power impact the image clarity?

the more resolving power, the clearer the image is

what is rayleigh’s criterion?

• how close 2 points can be and still be distinguished

• a way of calculating angular resolution;

• θ = λ / D

θ - angular resolution

λ - wavelength of light

D - diameter of circular aperture

when is the resolution of 2 objects not possible?

if the central spot of either image lies inside the first dark ring of the other image

DIAGRAM

what happens if the central spot of either image lies inside the first dark ring of the other image?

resolution of the 2 objects is not possible

DIAGRAM

why do we only care about the first rings of each light’s diffraction pattern?

because it’s the only one that determines resolution; with any more overlap, it is one singular light. with any less overlap (i.e., they’re not touching), then it’s 2 distinct lights

which lens do we use to diffract light?

convex

why do we use a convex lens to diffract light?

what is the diffraction pattern when the angular separation > λ / D ?

first rings are just overlapping

DIAGRAM

which angular separation produces this pattern?

DIAGRAM

angular separation > λ / D

when angular separation > λ / D , are the images easily resolved or not?

DIAGRAM

easily resolved

why are images of angular separation < λ / D able to be resolved the easiest?

because they are only just overlapping maybe go into more detail?

what exactly does angular separation > λ / D mean?

the angular separation is larger than the minimum angle separation the 2 points can have while still being distinguishable, meaning the images are easily resolved as the outer rings are only just overlapping

what image is produced when the light sources have an angular separation > λ / D ?

HERE

what is the diffraction pattern when the angular separation = λ / D ?

gulp

here

which angular separation produces this pattern?

DIAGRAM

angular separation = λ / D

when angular separation = λ / D , can the images be resolved or not?

DIAGRAM

they can be resolved, but only just

why are images of angular separation = λ / D only just able to be resolved?

what exactly does angular separation = λ / D mean?

what image is produced when the light sources have an angular separation = λ / D ?

what is the diffraction pattern when the angular separation < λ / D ?

which angular separation produces this pattern?

DIAGRAM

when angular separation < λ / D , are the images easily resolved or not?

DIAGRAM

why can’t images of angular separation < λ / D be resolved?

what exactly does angular separation < λ / D mean?

what image is produced when the light sources have an angular separation < λ / D ?

which angular separation is the easiest to resolve?

angular separation > λ / D

which angular separation is able to be resolved, yet only just?

angular separation = λ / D

which angular separation cannot be resolved?

angular separation < λ / D