The Speed of Waves on a Stretched Strings
●The speed of a wave traveling on a
stretched string of mass per unit length
μ and tension T is given by:
𝑻 𝒎 𝒎a𝒔𝒔
ν= 𝝁= =
𝝁 𝑳 𝑳𝒆𝒏𝒈𝒉𝒕
V :is the wave speed
●The wave speed v increases with increasing tension T. and the
wave speed should decreases as the mass per unit length μ of the
string increases.
The power, or rate of energy transfer, associated with the wave is
This expression shows that the rate of energy transfer by a
sinusoidal wave on a string is proportional to
(a) The square of the angular frequency,
(b) The square of the amplitude, and
(c) The wave speed.
Superposition of Waves
Law of Superposition:
If two or more traveling waves are moving through a medium, the
resultant value of the wave function at any point is the algebraic sum
of the values of the wave functions of the individual waves.
In Phase Out of Phase
Constructive interference Destructive interference
Light interactions with matter
• 1- Absorption
• This is when an EM wave disappears into a
medium by changing to keep energy.
• Darker Colors absorb EM waves
• Lighter Colors Reflect EM waves.
Only red light
White is reflected
light
White
light
Reflection and Refraction of
light wave
at
plane and Spherical Surfaces
• Ch (2) Converging and Diverging Lenses.
Wave Under Reflection.
Reflection law of light
When a light ray traveling in one medium encounters a boundary
with another medium, part of the incident light is reflected.
• Reflection of light.
Two types mirrors
plane Mirrors Curved(spherical) Mirrors
.
• Wave Under Refraction
Refraction of light :The direction of propagation of
light in the second medium changes
Refraction at Spherical Surfaces
Lens :is a portion of transparent refracting medium bounded by
two spherical surfaces or by one spherical surface and a plane
surface.
Thin lens:
It is a lens with a thickness (distance between the two refracting
surfaces) is negligible compared to the radii of curvature of the lens
surfaces
Types of thin lenses
Converging lenses Diverging lenses
convex lens Concave lens
A lens that is thick at the A lens that is thin at the
center and thin at the edges center and thick at the edges
Various lens shape
Converging lenses Diverging lenses
Refraction of Light.
1) Principle axis: It is the line joining the centers of
curvature of the two spherical surfaces ( i.e. XY)
2) Secondary axis : Al l ray path passing through a
lens and its optical center ( i.e. AB)
3)Optical center (P): It is a point on the principle
axis through which all the incident rays will
pass straight without any deviation
4)Center of curvature: The center of a sphere of part of which
a lens is formed.
5)Radius of curvature (R):The distance between the center
of curvature (c) and the curvature of that sphere.
5)Focus: It is the point at which the rays incident parallel to the
principle axis will meet.
6) Focal length (𝒇): The distance measured between the focus and
the optical center of the lens.
Refraction by curved surfaces.
R
h C1 f1 f2 C2
𝒉`
U V
U :The distance between object and lens
V :The distance between image and lens
h:The object height
hˋ:The image height
General law of lenses
Light passing through a lens experiences refraction at two surfaces.
The image formed by one refracting surface serves as the object for
the second surface and then let the thickness of the lens be
approximately zero.
n1 n2
R1 :is the radius of curvature
of the lens surface the light
from the object reaches first n
R2: is the radius of curvature of
the other surface of the lens.
n1 = n2 =1 because the lens is
surrounded by air U V
n : Refractive index of the lens
General law of thin lenses
𝟏 𝟏 𝟏 𝟏
+ = (𝒏 − 𝟏)( − )
𝑼 𝑽 𝑹𝟏 𝑹𝟐
The focal length f of a thin lens
𝟏 𝟏 𝟏
= (𝒏 − 𝟏)( − )
𝒇 𝑹𝟏 𝑹𝟐
Lens-makers’ equation
The thin lens equation, in air
𝟏 𝟏 𝟏
+ =
𝑼 𝑽 𝒇
General law of lenses
Principle focus(F): It is the point at which the rays incident parallel to
the principle axis will meet
Put U=∞ , 𝑽 = 𝒇
𝟏 𝟏 𝟏 𝟏
+ = (𝒏 − 𝟏)( − )
∞ 𝒇 𝑹𝟏 𝑹𝟐
𝟏 𝟏 𝟏
= (𝒏 − 𝟏)( − )
𝒇 𝑹𝟏 𝑹𝟐
In general
General law of lenses
Magnification(M)
𝑰𝒎𝒂𝒈𝒆 𝒉𝒆𝒊𝒈𝒉𝒕 𝒉′ 𝑽
𝑴= = =−
𝑶𝒃𝒋𝒆𝒄𝒕 𝒉𝒆𝒊𝒈𝒉𝒕 𝒉 𝑼
Lens Power(P)
Lens Power(P):
Is the degree to which a lens ,or other optical
system converges or diverges light, and it is equal
to the reciprocal of the focal length of the device
𝟏 𝟏 𝟏
P= = (𝒏 − 𝟏)( − )
𝒇 𝑹𝟏 𝑹𝟐
P=+ converging lens P = - Diverging lens
convex lens Concave lens
Sign Conventions for Thin Lenses 𝟏 𝟏 𝟏
+ =
𝑼 𝑽 𝒇
U= + real object U= - virtual object
V= + real image V= - virtual image
M= + erect image M= - inverted image
Real Image is inverted & Virtual image is erected
M> 1 magnify =Enlarged
image M< 1 diminished
M=1 equal
p, f= + convex lens p ,f = - concave lens
Refraction rules
C1 f1
f2 C2
C1 f2 f2 C2
Image formation by convex lens.
C1 f2 f1 C2
Case Position Position Size of Nature of
number of the of the image the image
object Image
Case(1) At infinity At the Highly Real and
focus(f) diminished inverted
(point –
size)
Image formation by convex lens.
C1 f2 f1 C2
Case Position of Position Size of Nature
number the object of the image of the
Image image
Case(2) Beyond)c( Between diminished Real
(f )and (c) and
inverted
Image formation by convex lens.
C1 f2 f1
C2
Case Position Position Size of Nature of
number of the of the image the image
object Image
Case(3) At )c( At (c) Same size Real and
inverted
Image formation by convex lens.
C1 f2 f1 C2
Case Position Position Size of Nature of
number of the of the image the image
object Image
Case(4) Between Beyond)c( Enlarged Real and
(f )and (c) inverted
Image formation by convex lens.
C1 f2 f1 C2
Case Position Position Size of Nature of
number of the of the image the image
object Image
Case(5) At (f ) At infinity Highly Real and
enlarged inverted
Image formation by convex lens.
C1 f2 f1 C2
Case Position Position Size of Nature of
number of the of the image the image
object Image
Case(6) Between In front of Enlarged Virtual
(p )and (f) the lens and
erect
Image formation by concave lens.
Case Position Position Size of Nature of
number of the of the image the image
object Image
Case(1) in In front of diminished Virtual
front of a the lens and
lens erect
Example(1)
A converging lens has a focal length of 10.0 cm. (a) an object is
placed30.0 cm from the lens. Find the image distance, and
describe the image.
Sol:
U=3o cm, convex, F= 10 cm ,V =?
𝑰𝒎𝒂𝒈𝒆 𝒉𝒆𝒊𝒈𝒉𝒕 𝒉′ 𝑽
𝟏 𝟏 𝟏 𝑴= = =−
+ = 𝑶𝒃𝒋𝒆𝒄𝒕 𝒉𝒆𝒊𝒈𝒉𝒕 𝒉 𝑼
𝑼 𝑽 𝒇
𝑽 𝟏𝟓
𝑴= − = − = -0.5
𝑼 𝟑𝟎
𝟏 𝟏 𝟏
+ =
𝟑𝟎 𝑽 𝟏𝟎
Real inverted
V=15 cm
diminished
