L23 : Resolving power of telescope - Wave Optics, Physics, Class 12 Video Lecture

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with part 23 so let us now talk about
some of the optical instruments and most
importantly we will talk about a
telescope and then about a microscope so
how does diffraction play an important
role in resolving power of telescope now
let us talk about the resolving power of
a telescope in our previous lesson we
have already seen that in telescope we
have two lenses one has the objective
and the other one has eyepiece so the
purpose of this objective is to create
an image at the focal point at the
second focal point of the objective and
the first focal point of the eyepiece
but this image which is created is an
inverted and diminished unit the purpose
of the eyepiece is just to magnify this
image so that we can view the object
which is a far-off object so now in this
case what do you think where is the role
of resolving power because the purpose
of eyepiece is mainly to magnify the
image so what do you think is the
purpose of the objective but it is the
purpose of objectives to resolve the
image that means let us suppose we are
doing two different stars so it is the
fact it is the work of objective to
resolve the two stars as two different
stars because if the objective does not
resolve an object then the eyepiece will
not be able to resolve it because I this
will just mad me right so it is object
is worth to resolve so what happens
normally so now let us focus only on the
objective so normally what happens
whenever a ray of light falls on the
objective it should get focused at the
particular point at a specific point but
what happens instead sometimes the
phenomenon of the
fraction comes into picture and whenever
diffraction occurs instead of getting
focused at a specific point it gets
focused to a spot that means it gets
focused in and around that area right so
these kind of diffraction effects take
place with the objective now before that
let us talk about two important terms
let us find limit of resolution and the
second one is resolving power
what does limit of resolution limit of
resolution is the angle subtended by the
distant objects on the object so now as
I told you it is the part of work of the
objective to resolve so now we will
focus our study on objective because
eyepiece has no role to play in deciding
the resolving power of a textbook so
what do I mean by little bit of
resolution it means how small and odd
check that telescope can lose what so we
will always want the telescope should
have a better resolving power so what is
a limit of resolution limit of
resolution means how small an object
that there is scope can resolve let us
suppose this limit of resolution is
generally defined as the angle subtended
by the distant objects on the object X
so you can say it is some angle which is
sent here right so now let us consider
an example it is suppose there are two
scenarios scenario a and scenario B in
scenario K we see that the limit of
resolution is 0.2 radians and in the
second case we say that the limit of
resolution is 20 radians that means
anything beyond anything below 20
radians that telescope cannot resolve so
that means the telescope can resolve
only up to 20 radians not beyond that
when I see that the resolving power is 0
for 2 radians that means it can resolve
up to an angle of 0.2
right that means lessen the limit of
resolution better if it is because if
the limit of resolution tells me how
small an object it can resolve so even
when the object is more small as it goes
away right the object if the object is
ten meters away from you and if the
object is hundred meters away from you
the one which is hundred meters away it
looks smaller right
so that means it is better if the
telescope is able to distinct very very
small images so that means it is always
preferable to have smaller value of
limit of resolution so we say that if
the limit the smaller is the value of
resolution the greater is the resolving
power of the telescope so the resolving
power of this telescope will be greater
than this one right so we see that
resolving power of a telescope is
inversely proportional to the limit of
resolution limit of resolution is
generally denoted by D theta right and
how do we find out the limit of
resolution this limit of resolution is
directly proportional to the wavelength
of light used and it is inversely
proportional to the diameter of the
objective or the aperture because
greater the diameter of the objective
more and more light can enter into it
now since if more and more light enters
into it the telescope will be able to
have more detailed information so it can
give it can add more detail information
to the image so it is always preferable
to have an objective of larger diameter
because if the diameter is large more
and more light will enter the better the
more the light enters the more detailed
information that is hope then you get
and it can produce detailed image so
because resolving power is all about
clearer image or detailed image so we
always prefer that the diameter of the
objective should be greater so that
means that limit of resolution is in
firstly proportional to the diameter and
it is directly proportional to the
wavelength so greater the wavelength
better is the limit of resolution right
so from this so with this we can
understand what is limit of resolution
now let us see what is resolving power
as mentioned before small at the limit
of resolution grated and stuff resolving
power so we say that resolving power is
proportional to 1 by D theta and D theta
is proportional to lambda by capital T
so we can say that so this D theta is
written as 0.6 sorry it is written as 1
point to 2 lambda divided by capital T
this is the limit of resolution so this
is the limit of resolution and now how
do I calculate the resolving power if
you look at it in this case this to a is
nothing but the diameter of the aperture
or the convex lens and F is its focal
length now what happens normally if
parallel beam of light is incident on
the convex lens it should get focused at
one single point but when diffraction
occurs now when diffraction will occur
diffraction occurs when the distances
measured here is comparable to the
wavelength of light so in that case what
happens instead of a single point a spot
appears what is this part this part is
nothing but a diffraction pattern
diffraction pattern which will have a
central maximum so you have this central
maximum which is surrounded by a dark
band that is minima then secondary
Maxima again the minima against
secondary maxima and so on this is how
you will get a pattern now what is the
radius and it has been experimentally
found that the radius of this central
band is found out to live 1.2 to lambda
divided by capital G like this has been
found as the center of the
region so if we want to have to clearly
resolve two different objects what is
what is our desirable resolving power
for the telescope as we can see here we
would want the resolving power of the
telescope to the proportional to D
divided by 1.2 to lambda where D is the
diameter of the lens right so you
understood how diffraction plays an
important role in determining the
resolving power of telescopes because
with the help of diffraction we can
calculate the radius of this central
region right because we get a spot so we
find out the central maximum or the
position or width of the central maximum
using the diffraction phenomenon pattern
so once we get that we can find out the
limit of resolution from there only we
got this limit of resolution and
thereafter the resolving power of a
telescope let us now talk about so okay
so what does the conclusion here a
telescope must have a large diameter
objective for better resolution thank
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