L29 : Sign convention in lens - Ray Optics, Physics, Class 12 Video Lecture

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with part 29 now let us look at the sign
Convention for lens I will just show you
four scenarios which will clear clear
out the concept for the Convention which
we follow regarding sign in case of an
lens so let us first look at upon its
lens so this is a convex lens let us
suppose we have an object here this is
my optical center oh so a ray of light
from the object after refraction it goes
and cuts it here so here we get the
image right so now what would be the
sign for imaged object distance image
distance focal length and radius of
curvatures so what will be the image
distance I'm sorry
object distance the object lies towards
the left that means it is off this is
the direction of the incident rate so
the incident ray is moving in this
direction right so we are measuring the
distance of the object from optical
Center which is in this direction so it
is opposite to the direction of incident
ray so it would be negative what about
the image distance image distance we are
measuring towards this direction which
is along the same direction as incident
ring so it would be positive what would
be the focus focus when we talk about we
talk about the second focal point that
means the point where the ray of light
converge after refraction so we saw that
in case of a convex lens the ray of
light this is how it happens in case of
a convex lens the ray of light after
reflection diffraction they meet at this
point so the focal point lies along this
direction so the focal point will be
positive what would be odd one let us
assume this is one this their face is
true so r1 is the radius for this
medical settings so it's radius will lie
somewhere on this side
similarly r2 will lie somewhere on this
side right so r1 would be positive and
r2 will be negative
correct okay so now you just look at a
concave lens so in case of concave lens
also let us assume this surface or
surface one this as step is to let us
say this is some object or a ray of
light falls on this lens and then it
gets diverged right so the point where
it is it virtually meets the principal
axis the image is formed there all right
so in this case what happens you V f r1
and r2 so in this case the object
distance so here also the direction of
incident ray is this so you is opposite
to the direction of incident rate so
negative V is again opposite to the
direction of incident ring so negative
focus what happens in case of a concave
mirror in case of a concave mirror ray
of light parallel gets diverged but they
seem to appear this they seem to me that
at this point so the focus line on the
left hand side so their focus in case of
a convex lens is a concave lens's again
negative what about R 1 R 1 is this
surface so the radius for this spherical
surface will lie somewhere on this side
and the radius for this spherical
surface R 2 will lie somewhere on this
side so here R 1 is negative and R 2 is
positive right so here I am just giving
you the sign convention for different
types of lenses so that you do not get
confused by solving problems now let us
look at a convex lens again such that
the ray of light
is coming from some infinite object so
let us suppose some ray of light is
coming this way it falls on the lens and
after refraction it meets the principal
axis here so in this case where is where
is the object we join it virtually and
we see that it looks like that the
object would have been somewhere here so
in this case what would be the sign
convention u v f r1 and r2 in this case
the distance of the object the object is
located on this side so it would be
positive because here also the direction
of the incident ray is this distance of
the image is again positive focal length
is positive and one if we call this as 1
and this as 2 so r1 will be positive and
r2 will be negative right because I have
to realize somewhere here and r1 will
lie somewhere here right okay now let us
look at this on Fitz concave lens here
this is upon cave surface and this is a
convex surface right so let us look at
this convex concave lens convex or
concave lens okay so in this case let us
assume that the object lies somewhere
here so what happens when the Ray goes
here it gets diverted in this way so we
can extrapolate it and we can say that
an image will be formed somewhere here
so in this case what could be the sign
convention for each of these values what
is U the direction of incident ray is
the same so you will be negative V will
also be negative
what would they focal length in this
case because it is neither a convex lens
nor upon keep lens but if you look at it
the radius of curvature of the convex
lens will lie in this direction
similarly the radius of curvature of the
concave lens will also lie somewhere
around this direction let me call this
as 1 this as 2 so if this is R 1 this
should be R 2 so R 1 is greater than R 2
like both are positive so R 1 and R 2
both are positive and if we see R 1 is
greater than R 2 so that means the
convex lens is dominating here right
because it has more radius of curvature
so what will happen when the parallel
rays of light will come here instead of
diverging they will get converged at a
point so therefore since the convex lens
is dominating here therefore the focus
here will be positive but if the concave
lens would have had greater radius of
curvature in that case the focal length
would have been negative so in this case
the focal length will be positive so
this is how we decide about the sign
convention for different from different
types of lenses also you can if you want
you can study about the image formation
by lenses for objects located at
different points we have already
discussed that in the case of spherical
mirrors the rules will still be the same
and using the same logic and same
concepts you can try out to find out the
position and the nature of the image
formed by a different location of
objects in front of the lens thank you
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