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MASTER CARD
OPTICS
1. Reflection and Refraction of light
2. Total internal reflection and optical fibre
3. Refraction through a prism
4. Scattering of light
5. Defects of vision
6. Optical instruments
7. Wave fronts and Huygen’s principle
8. Interference
9. Diffraction
10.Polarisation
RAYOPTICS
REFLECTION AND REFRACTION
1. Reflection – When a light ray is incident on a smooth surface it
bounces back to the same medium . This is called Reflection.
2. Laws of reflection –
a. Angle of incidence is equal to the angle of reflection.
b. Incident ray , normal and reflected ray all lie in the same plane.
3. Mirror formula
1/f = 1/u +1/v
Where f- focal length , u – distance of object
v- distance of image
4. Magnification of mirror : m= -v/u = - f/ (u-f) =I/O
5. Refraction – When a ray of light goes from one medium to
the other medium , there is a change in speed and direction of the ray
This phenomenon is called Refraction .
6. Laws of refractiona. The incident ray , normal and refracted ray all lie in the same plane.
b. The ratio of sine of angle of incidence to sine of angle of refraction is
constant. ( Snell’s law)
7. Lens formula : 1/f = 1/v – 1/u
8. Magnification of lens : m = v/u = f/(u+f)
9. Lens maker’s formula :
A
O
P2
22
p1
I
I`
B
If R1 and R2are the radii of curvature of first and second refracting surfaces of a thin lens of focal
length f . Let O is a point object as shown –
For refraction at surface AP1B : n2/v` -n1/u = (n2 – n1) / R1 -------(1)
For refraction at surface AP2B : n1/v – n2/v` = (n1 – n2) /R2 -------(2)
Adding equation 1 and 2
1
1/v – 1/u = ( n2 – 1) (1/R1 – 1/R2)
1
Or 1/f = ( n2 – 1) (1/R1 – 1/R2)
This is known as lens maker’s formula.
10.Lens Formula :
A
N
F
E
C
B
D
From the fig.
AB/DE=BC/EC---------(1)
And ∆NCF~∆DEF
AB/DE/=CF/EF----------(2) (NC=AB)
From 1&2, We have
BC/EC=CF/EF
-u/v=f/v-f
Or, vf=-uv+uf
Or, uv=uf-vf
Hence 1/f=1/v-1/u
This is called lens formula.
10.
COMPOUND MICROSCOPE :
Magnifying power
m=-v0/u0 (1+D/fe)
vo
E
O
Fo
Fe
uo
ue
11.
Astronomical telescope :
Magnifying power (normal adjustment)
m = -fo/ fe
Magnifying power (least distance of distinct vision)
m = -fo/ fe (1+ fe/D)
Total Internal Reflection
When angle of incidence in denser medium is greater than critical angle then ray of
light is reflected back into the same medium. This phenomenon is known as total internal reflection.
Condition of TIR
1.The ray of light must pass from denser to rarer medium .
2. The angle of incidence must be greater than critical angle. (i.e.i>ic)
3.Relation between refractive index and critical angle.
by snell’s law sin i/sin r =1/μ
or sin c/sin r = 1/μ
or sin c /sin 90= 1/μ
or sin c = 1/μ or μ = 1/sin c
5.Optical fibers- A device based on TIR by which a light signal may be transmitted from one
place to another without any loss of energy is called an optical fiber. It is used in medical field
and telecommunication.
6.to invert the image
i) through 90˚
ii) through 180˚
Dispersion of light- The phenomenon of splitting of white light into its constituents colour is
called dispersion of light .
Prism- The device used for dispersion of light is called prism
Refraction due to prism
Angle of deviation is the angle through which incident ray turned by the prism while
passing through it.
Sum of the angle of deviation and angle of prism is equal to the sum of incident
angle and angle of emergence. δ +A =i +e
Deviation produced by a prism δ =( n – 1)A
δ is angle of deviation , n is refractive index of prism , A is angle of prism
A
δ
i
Prism formula :
n =( sin (A + δm)/2) / sin (A/2)
Scattering of light :
According Lord Rayleigh :
4
The intensity of scattered light
I α 1/λ
As wavelength of blue colour is least and wavelength of red colour is the most , so blue
colour scatters the most and red colour scatters the least.
Red appearance of sun during sunrise and sunset --At the time of sunrise and sunset light travels the larger path in atmosphere while reaching
our eyes and blue colour scatters the most whereas red colour sctters the least , so only red
colour reaches our eyes and sun appears reddish.
Blue appearance of sky :
When sunlight travels through the atmosphere blue colour scatters the most whereas red
colour scatters the least, so sky appears blue in colour.
Defects of vision : there are mainly 3 defects of vision
1. Myopia 2. Hypermetropia 3. Presbyopia
MYOPIA : In this defect a person can see clearly only nearby objects but unable to see
Clearly the faraway objects.
The cause of this defect is 1. decrease of focal length of the eye lens
2. elongation of the eyeball.
HYPERMETROPIA : In this defect a person can see clearly only faraway objects but
unable to see clearly the nearby objects.
The cause of this defect is 1. increase of focal length of the eye lens
2. contraction of the eyeball.
PRESBYOPIA:
In this defect a person can not see clearly both nearby and faraway objects
The cause of this defect is 1. weakening of ciliary muscles.
2. decrease in elasticity of eye lens.
WAVEOPTICS
1. Wavefront: A wavefront is defined as the continuous locus of all the particles of a
medium vibrating in the same phase.
2. Huygen’s principle :
a. Every point on a given wavefront acts as a fresh source of new disturbance called
secondary wavelets which travels in all directions with the velocity of light.
b. A surface touching these secondary wavelets tangentially in forward direction at any
instant gives secondary wavefront at that instant.
3. Superposition principle :
The principle of superposition states that whenever two or more waves traveling in same
direction superpose , the total displacement (Y) at any points equal to the vector sum of
individual displacements at that point.
Y= Y1 + Y2 + Y3 + --------+ Yn
6. Interference : When two waves of same frequency and same phase superposed on each
other then a pattern of maxima and minima is formed . This pattern is called as interference
pattern.
7. condition for interference: 1. sources should be coherent
2. two coherent sources should be every closed to each other.
8. Resultant intensity at a point on the screen
I = k (a12+a22 + 2a1 a2 cos φ )
where a1 , a2 are amplitudes of interfering waves and φ is the phase difference between
them
9. Conditions for maxima and minima :
s1
S
2
D
Path difference
x = yd/D
Where y is position of fringe
D is distance between slits and screen
d is distance between slits
condition for maxima :
φ = 2nπ
where n = 0, 1,2,……..
x = nλ
Imax = k (a1+a2)2
condition for minima :
φ = (2n-1)π
where n = 0, 1,2,……..
x = (2n-1)λ/2
Imin = k (a1-a2)2
Imax/ Imin = (a1+a2)2 / (a1-a2)2
10. Position for maxima : yd/D = nλ
y = nDλ/d
Position for minima : yd/D = (2n-1)λ/2
y = (2n-1)Dλ/2d
11.Fringe width (β) : Separation between the centres of two consecutive maxima or two
consecutive minima is called as fringe width.
β = λD/d
12. Diffraction : It is phenomenon of bending of light waves after passing through a small
aperture / obstacle and reaching in the regions of shadow.
Single slit diffraction pattern : It consist of central bright band surrounded on either side by
alternate dark and bright bands with decreasing intensity.
Half angular width of the central bright band
θ = λ/a = x/ D
where λ is wavelength of light
a is width of slit
x is half linear width of central maxima (x = λD/a)
D is distance between slit and screen
14. Unpolarised or ordinary light :In such light oscillation of electric field occur in all
directions in a plane perpendicular to the direction of light propogation.
15. Polarisation : It is the phenomenon in which electric vectors of light restricted to a
particular plane after passing through a nicol prism or tourmaline crystal.
The phenomenon of polarisation proves that light is transverse in nature.
16. Brewster’s law : μ = tan ip
Where μ is refractive index of material
ip is polarizing angle
At polarising angle reflected ray and refracted ray are perpendicular to each other.
17. Malus law : It states that if polarized light is passed through an analyser , the intensity
of light transmitted is directly proportional to cos2θ where θ is angle between planes of
polariser and analyzer.
18. Polaroid : A Polaroid is a device to produce and detect plane polarised light .
Some uses of polaroids :
1.Sun glasses filled with Polaroid sheets protect our eyes from bright sunlight
2.Polaroid reduces head light glare of vehicles.
3. Polaroids are used in 3D films.