Advertisements
Advertisements
प्रश्न
Discuss the interference in thin films and obtain the equations for constructive and destructive interference for transmitted and reflected light.
Advertisements
उत्तर
- Interference in thin films:
- Let us consider a thin film of transparent material of refractive index p (not to confuse with an order of fringe n) and thickness d. A parallel beam of light is incident on the film at an angle i.
- The wave is divided into two parts at the upper surface, one is reflected and the other is refracted. The refracted part, which enters into the film, again gets divided at the lower surface into two parts; one is transmitted out of the film and the other is reflected back into the film.
Interference in thin films
- For transmitted light:
- The light transmitted may interfere to produce a resultant intensity. Let us consider the path difference between the two light waves transmitted from B and D. The two waves moved together and remained in phase up to B where splitting occurred.
- The extra path travelled by the wave transmitted from D is the path inside the film, BC + CD. If we approximate the incidence to be nearly normal (i = 0), then points B and D are very close to each other. The extra distance travelled by the wave is approximately twice thickness of the film, BC + CD = 2d. As this extra path is travelled in a medium of refractive index p, the optical path difference is,
δ = 2μd. - The condition for constructive interference in transmitted ray is,
2μd = nλ
Similarly, the condition for destructive interference in transmitted ray is
2μd = (2n-l) `λ/2`
- For reflected light:
- Wave while travelling in a rarer medium and getting reflected by a denser medium, undergoes a phase change of n or an additional path difference of `λ/2`.
- Let us consider the path difference between the light waves reflected by the upper surface at A and the other wave coming out at C after passing through the film.
- The additional path travelled by wave coming out from C is the path inside the film, AB + BC. For nearly normal incidence this distance could be approximated as, AB + BC = 2d. As this extra path is travelled in the medium of refractive index p, the optical path difference is, δ = 2μd.
- The condition for constructive interference for reflected ray is,
2μd + `λ/2` = nλ (or)
2μd = (2n – 1) `λ/2` - The additional path difference λ/2 is due to the phase change of n in rarer to denser reflection taking place at A. The condition for destructive interference for a reflected ray is,
2μd + `λ/2` = (2n + l)`λ/2` (or)
2μd = nλ
APPEARS IN
संबंधित प्रश्न
Four light waves are represented by
(i) \[y = a_1 \sin \omega t\]
(ii) \[y = a_2 \sin \left( \omega t + \epsilon \right)\]
(iii) \[y = a_1 \sin 2\omega t\]
(iv) \[y = a_2 \sin 2\left( \omega t + \epsilon \right).\]
Interference fringes may be observed due to superposition of
(a) (i) and (ii)
(b) (i) and (iii)
(c) (ii) and (iv)
(d) (iii) and (iv)
A narrow slit S transmitting light of wavelength λ is placed a distance d above a large plane mirror, as shown in the following figure. The light coming directly from the slit and that coming after the reflection interfere at a screen ∑ placed at a distance D from the slit. (a) What will be the intensity at a point just above the mirror, i.e. just above O? (b) At what distance from O does the first maximum occur?
A long narrow horizontal slit is paced 1 mm above a horizontal plane mirror. The interference between the light coming directly from the slit and that after reflection is seen on a screen 1.0 m away from the slit. If the mirror reflects only 64% of the light energy falling on it, what will be the ratio of the maximum to the minimum intensity in the interference pattern observed on the screen?
In a Young’s double-slit experiment, the slit separation is doubled. To maintain the same fringe spacing on the screen, the screen-to-slit distance D must be changed to ______.
One of Young’s double slits is covered with a glass plate as shown in figure. The position of central maximum will,
How do source and images behave as coherent sources?
Light of wavelength 600 nm that falls on a pair of slits producing interference pattern on a screen in which the bright fringes are separated by 7.2 mm. What must be the wavelength of another light which produces bright fringes separated by 8.1 mm with the same apparatus?
In Young's double-slit experiment, if the width of the 2nd bright fringe is 4 x 10-2 cm, then the width of the 4th bright fringe will be ______ cm.
A wire of length 'L' and area of cross-section · A' is made of material of Young's modulus 'Y'. It is stretched by an amount 'x'. The work done in stretching the wire is ______.
In Young's double slit experiment with a source of light of wavelength 5860 Å, the first maxima will occur when ____________.
Two coherent light sources of intensity ratio 'n' are employed in an interference experiment. The ratio of the intensities of the maxima and minima in the interference pattern is (I1 > I2).
If two waves represented by `"y"_1 = 3 "sin" omega "t"` and `"y"_2 = 5 "sin" (omega "t" + pi/3)` interfere at a point, then the amplitude of the resulting wave will be about ____________.
Two identical light sources s1 and s2 emit light of same wavelength `lambda`. These light rays will exhibit interference if their ______.
The graph shows the variation of fringe width (β) versus distance of the screen from the plane of the slits (D) in Young's double-slit experiment Keeping other parameters the same. The wavelength of light used can be calculated as d = distance between the slits ______
Waves from two coherent sources of light having an intensity ratio I1 : I2 equal to 'x' interfere. Then in the interference pattern obtained on the screen, the value of (Imax - Imin)/(Imax + Imin) is ______
In the biprism experiment, a source of monochromatic light is used for a certain distance between slit and eyepiece. When the distance between two virtual sources is changed from dA to dB, then the fringe width is changed from ZA to ZB. The ratio ZA to ZB is ______
In an interference experiment, the intensity at a point is `(1/4)^"th"` of the maximum intensity. The angular position of this point is at ____________.
(cos 60° = 0.5, `lambda` = wavelength of light, d = slit width)
A beam of electrons is used in Young's double-slit experiment. If the speed of electrons is increased then the fringe width will ______.
In a biprism experiment, fifth dark fringe is obtained at a point. A thin transparent film of refractive index ‘μ’ is placed in one of the interfering paths. Now 7th bright fringe is obtained at the same point. If ‘A’ is the wavelength of light used, the thickness of film is equal to ______.
