

CLASS11 PHYSICS
Reflection through the plane and Curved Surface.
1. Glancing angle (g): The angle between incident ray and reflecting surface is called glancing angle.
In figure: < AOX is the glancing angle.
2. Deviation angle (δ): The angle between the reflected ray of light and original path of light produced
back is called
Deviation angle.
In figure: < BOC is the deviation angle.
3. Relation between glancing angle and deviation angle (g and δ):
< BOC=δ
δ = < BOY + < YOC
δ = < NOY  < NOB + < YOC
δ = 90^{0} r + g [< XOA=< YOC Vertically Opposite Angle]
But,
< AON=< NOB [From law of reflection]
i=r
90^{0}i+g
[90i+g]
g+g
2g
Law of rotation of light:
When mirror is rotated by an angle keeping the incident ray fixed then reflected ray
of light rotates by an angle
2θ. This is called law of rotation of light.
Let us consider XY is a plane mirror. Let, AO is the incident ray which reflects
along OB.
Let, mirror is rotated by an angle ; then incident ray reflect along OB^{'}
as shown in figure.
Let, be the glancing angle.
Then from figure,
< BOC=δ_{1}= 2g
< B^{'}OC = δ_{2}= 2(g+θ)
Again from figure,
β= < B^{'}OB = < B^{'}OC  < BOC
β= 2(g+θ)2g
β= 2g+2θ2g
β= 2θ
Types of image:
1. real image: inverted, virtual object.
2. virutal image: erect, real object
1. Real image: The image which is obtained by the actual
intersection of reflected ray of light or the
refracted ray of light is called real image. It can be produced
on screen and it is always inverted.
The real image can be obtained by the plane mirror when the
object is virtual which is shown in figure.
2. Virtual image: An image which cannot be obtained on a screen
is called virtual image. It is formed
when the light rays after reflection do not actually intersect
but intersect when produced backward.
The light rays appear as coming from an image. The virtual image
is erect or upright with respect
to the object.
Image formed by Plane Mirror:
The image formed by plane mirror is same in size i.e. image
distance and object distance are equal.
Let us consider, XY be the plane mirror. Let O be the object.
Let OA is the incident ray of light incident normally which
reflect along AO.
Let OB be the another incident ray which reflect along BC. Now,
let us draw a normal at point B as shown in figure.
Again, let us draw AO and BC back to meet at point I which is
virtual image.
Now,
1. < OBn=< nBC [From law of reflection]
2. < AOB=< OBn [alternate angle]
3. < AIB=< nBC [Corresponding angle]
4. < AOB=< AIB [From statement 1 and 2] and < OAB=<
IAB [Right angle]
5. AB = AB [common side]
OAB and AIB are congruent. So, OA=AI. This means
object distance is equal to image distance.
Relation Between Focal length and Radius
of Curvature:
Let us consider a concave mirror of small
apperature with focal length (F). Let OA is the
incident ray of light incident parallel to
the principal axis at point A which reflects
passing through the focus as shown in figure.
Let us draw a normal passing through the centre
of curvature at point A.
< OAC=< ACF [alternate angle]
< OAC=< CAF [law of reflection]
< ACF=< FAC
CF=FA [CAF= isosceles triangle]
CP= R= CF+FP = CF+f
FA+f
Since mirror is small in apperature
A lies very closed to P. So, we can
write,
PF FA
R= F+F = 2F
This shows that focal length of
mirror depend only with a radius of
curvature.
Mirror formula for
concave mirror when
image form is real.
(A^{'}B^{'})/LN =
(A^{'}F)/FN
(A^{'}B^{'})/AB =
(A^{'}F)/FN < (i)
(A^{'}B^{'})/AB
= (A^{'}C)/AC <
(ii)
From equation (i) and
equation (ii)
(A^{'}F)/FN =
(A^{'}C)/AC
< (iii)
PA^{'}= v , PC=
R
PA= u , PF= f
Again from figure,
A^{'}C=
PCPA^{'}
AC= PAPC
A^{'}F=
PA^{'}PF
Now equation (iii)
becomes,
[(PCPA^{'})/(PAPC)
= (PA^{'}PF)/F]
Taking sign convention,
(Rv)/(uR) = (vf)/f
or, (2fv)/(u2f) =
(vf)/f [since, R=2f]
2f^{2}vf =
uv2vfuf+2f^{2}
or, vf = 2vf + uf  uv
or, vf = uv  uf
or, (vf/uvf) = (uv/uvf)
 (uf/uvf)
1/u = 1/f  1/v
therefore, 1/f = 1/u
+ 1/v
Mirror
formula for
convave
mirror when
image formed
is virtual
AP= u= object distance
A^{'}P= v=
image distance (image is
virtual)
A^{'}B^{'}=
h_{1}= height of
the image
AB= h_{0}= heigh
of the object.
FP= f= focal length of
the mirror.
From figure, In ΔBAP and
ΔB^{'}A^{'}P
are similar triangles.
So,
(A^{'}B^{'})/AB
= (A^{'}P)/AP
(A^{'}B^{'})/AB
= v/u < (i)
In
ΔB^{'}A^{'}F
and ΔMNF are similar
triangles. So,
A^{'}B^{'}/MN
= A^{'}F/FN
Here, MN=AB and
FN≃FP, we have
(A^{'}B^{'})/AB
=
(A^{'}P+FP)/FP
(A^{'}B^{'})/AB
= (v+f)/f =
(vf)/f <
(ii)
Equating
equation (i) and
equation (ii)
v/u = (vf)/f
vf = uv+vf
Dividing both
sides by uvf, we
get
uv/uvf =
(uf/uvf) +
(vf/uvf)
1/f = 1/v + 1/u
therefore,
1/f = 1/u +
1/v
This is the
expression of
mirror formula.
Linear
Magnification
It is defined as
ratio of image
distance to the
object distance.
It is denoted by
'm'.
i.e. m= v/u
Also, linear
magnification is
defined as the
ratio of size of
image to the
size of object.
i.e. M= I/O (no
unit.)
1. When m= 0
this means the
image is point
in size.
2. When m= 1
this means image
distance is
equal to the
size of object.
3. When m < 1.
4. When m >
1.
5. m= +ve,
the image is
real.
6. m= ve,
the image is
virtual.
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