Wave Optics

Question 1

Wavefront is
1) Definition :
2) Perpendicular to :

Answer 1

1) Point vibrating in same phase is called wavefront

2) Perpendicular to direction of propagation of wave or direction of ray

Question 2

Point source

Answer 2

Spherical wavefront

Question 3

Linear source

Answer 3

Cylindrical wavefront

Question 4

Prism

Answer 4

Planar wavefront

Question 5

Huygen’s principle states that :

Answer 5

Each point of wavefront emerging from the primary wavefront acts as a source of light and other wavelet emerge from it…These wavelet are referred as Secondary wavefront

Question 6

Tangent to secondary wavelet gives

Answer 6

New position of next wavefront at later time…t

Question 7

Superposition of Waves

Answer 7

Resultant displacement produced by no. of waves is vector sum of displacement produced by each of the waves

y = y1 + y2 + y3…..

Question 8

Coherent sources

Answer 8

Sources with :

△ ∅ or ∅ = 0 or constant

Question 9

Interference

Answer 9

_Superpostion of wave with same frequency & same wavelength

Y1 = A1 sin ( wt - kx )
Y2 = A2 sin ( wt - kx + ∅ )

k = 2π / λ
w = 2 π f
∅ = phase diff / waves

• Interference is just a redistribution of energy
• The total energy remains constant during interference

Question 10

Resultant amplitude = A = ?

Answer 10

A = √ (A1)² + (A2)² + 2 ( A1 * A2 ) cos ∅

Question 11

Resultant intensity = I = ?

Answer 11

I = (I 1)² + (I 2)² + 2 √ ( I1 * I2 ) cos ∅

Question 12

Relation b/w Intensity and Amplitude

Answer 12

I ∝ A²

Question 13

Phase difference = △∅ = ?

Answer 13

△∅= 2 π * △ x / λ

         Or

∅= 2 π * x / λ

{ △x or x = Path difference }

Question 14

For identical sources :
1) I = ?
2) A = ?

Answer 14

1) I 1 = I 2 = I °

I = 4 I° cos² ( ∅ / 2 ) 

2) A1 = A2 =A°

A = 2 A° cos ( ∅ / 2 )

Question 15

Constructive interference

Answer 15

Same amplitude and same direction

Cos ∅ = + 1

∅ = +_ 2n π { n = 0 , 1 , 2 , 3…. }

▪︎ EVEN MULTIPLE OF π

△x = +_ n λ { n = 0 , 1 , 2 , 3…. }

A ( max ) = A1 + A2
I ( max ) = ( √ I 1 + √ I 2 )²

▪︎ Identical sources

A ( max ) = 2 A°
I ( max ) = 4 I°

Question 16

Destructive interference

Answer 16

Same amplitude & opposite direction

Cos ∅ = - 1

∅ = +_ ( 2n-1 ) π { n = 1 , 2 , 3…. }

▪︎ ODD MULTIPLE OF π

△x = +_ ( n-1) λ /2 { n = 1 , 2 , 3…. }

A ( min ) = A1 - A2
I ( min ) = ( √ I 1 - √ I 2 )²

▪︎ Identical sources

A ( min ) = 0
I ( min ) = 0

Question 17

Young’s double slit experiment :

1) Path difference
2) Constructive interference
3) Destructive interference
4) Fringe width
5) Angular width

Answer 17

1) △ x = y d / D

2) y = +_ n D λ / d

3) y = +_ ( 2n - 1 ) D λ / 2 d

4) β = D λ / d

5) θ = λ / d
___ Angular width is independent of D

λ = wavelength
D = Screen distance
d = dist b/w slits

Question 18

YDSE with white light

Answer 18

White light _ all colours

Hence , white light _ △ x = 0 ( doesn’t depend on wavelength for central maxima

Question 19

YDSE in water :

1) Fringe width in water ?
2) wavelength in water ?

Answer 19

1) β’ ( water ) = β ( air ) / μ

  { β ( air ) = D λ / d } 

2) λ’ ( water ) = λ ( air ) / μ

   { β ∝ λ }

Question 20

Shift in central maxima and entire pattern by same distance cuz of glass slab is__ ?

Answer 20

y = ( μ - 1 ) t D / d

Question 21

Diffraction

1) Simple definition
2) Fresnal diffraction
3) Frouhofer diffraction
4) Maxima
5) Central maxima
6) Minima

Answer 21

1) Bending of light rays

2) Fresnal diffraction
Screen and source at finite dist

3) Frouhofer diffraction
Screen and source at infinite dist

4) Maxima
θ = +_ n λ / a
β = D λ / a

5) Central maxima
θ = +_ 2 λ / a
β = 2 D λ / a

6) Minima
θ = +_ ( 2n + 1 ) λ / 2a

{ a = slit width )

Question 22

Fresnal diffraction
1) if D < Z (f)
2) if D > Z (f)
3) Z(f) = ?

Answer 22

1) Particle nature

___ RAY OPTICS DOMINATE

2) Wave nature

___ WAVE OPTICS DOMINATE

3) Z(f) = a² / λ

Question 23

Resolving power

Answer 23

Ability of an instrument to distinguish b/w two neighboring points

Resolving power ∝ diameter of lens
∝ 1 / Resolving limit

Question 24

Resolving power
1) Telescope
2) Microscope

Answer 24

1) R.P = 1 / R.L = 2a / 1.22 λ = 1 / θ

2) R.P = 1 / R.L = 2 μ sin θ / 1.22 λ = d

Question 25

Polarization
1) Definition
2 ) Intensity before passing through polarizer
3) Intensity after passing through polarizer
4) Intensity after passing through analyser
5) Law of malus

Answer 25

1) Restricting vibration of light in a particular direction perpendicular to the direction of propagation of wave is called polarization of light

2) I°

3) I 1 = I° / 2

4) I 2 = I 1 cos ² θ

5) I 2 = I 1 cos ² θ

Question 26

Polarization by scattering

Answer 26

__Sunlight gets scattered cuz of small particles such as dust in atmp and it is absorbed by e- in molecules and hence e- start vubrating

These vibrating e- emit radiation in all direction except in it own line of vibration

Question 27

Polarization by reflection

Answer 27

At 90° angle of reflected ray to refracted ray :

• Reflected ray is completely polarized
• Refracted ray is partially polarized

▪︎ Brewster’s angle or polarization angle = tan θ (p) = μ

▪︎ 45° > θ < 90°