Physics IV Sem Chapter 4 – Interference (Important Questions) Two Marks Questions: 1) What is interference of light? The modification in the distribution of light energy due to the super position of two or more waves of light is called Interference of Light. 2) What are the coherent sources? Any two sources of light continuously emitting light waves of the same amplitude, frequency, wavelength and having zero or constant phase difference are called Coherent sources. 3) What is division of wavefront? In this case a monochromatic light is emerging from a narrow single slit, then passing it through two slits by side. The two parts of the same wavefront travel through different paths and reunite on a screen to produce fringe pattern. This is known as interference due to division of wavefront. 4) What is the division of amplitude? The amplitude of light wave is divided into two parts, namely reflected and transmitted components, by partial reflection at a surface. The two parts travel through different paths and reunite to produce interference fringes. This is known as Interference due to division of amplitude. 5) What is the path difference for maxima in case of interference in thin film due to reflected light. If the path difference is x=m𝜆 where m=0,1,2,3,4………. etc. constructive interference takes place and the film appears bright. 6) What is the path difference for minima in case of interference in thin film due to reflected light. If the path difference is x=(2m+1) 𝜆 /2 where m=0,1,2,3……...etc. destructive interference takes place and the film appears dark. 7) Write the expression for the path difference for maxima and minima in case of interference in thin film due to transmitted light. Path difference for maxima bright: 2nt cos r = m𝜆 where m = 0,1,2,3, . . .. etc. Path difference for minima dark: 2nt cos r = (2m+1) 𝜆 /2 where m = 0,1,2,3, . . .. etc. 8) Write the expression for the fringe width in case of wedge-shaped film. The fringe width in case of wedge-shaped film is, 𝛽= 𝑥2 −𝑥1 𝑘 = 𝜆 2𝑛𝜃 9) What are Newton's rings? Newton's rings are a phenomenon in which an interference pattern is created by the reflection of light between two surfaces; a spherical surface and an adjacent touching flat surface. 10) Write the expression for the diameter of bright and dark rings in case of interference due to reflected light. Diameter of bright rings, dm = √(2𝑚 − 1)2𝑅𝜆 1 Diameter of dark rings, dm 𝛼 √𝑚 11) What is the principle of Michelson's interferometer. The amplitude of the light beam from an extended source is divided into two parts of equal intensities by partial reflection and refraction. These beams are sent in two directions at right angles and are brought together after reflection from plane mirrors to produce interference fringes. 12) Mention two uses of Michelson's interferometer. 1) Determination of Wavelength. 2) Determine the thickness of a thin transparent sheet. Five Marks Questions 1) Obtain an expression for determination of thickness of thin film using biprism. 2 2) Derive the expression for the optical path difference in thin films due to reflected light. 3 4 3) Derive the expression for the optical path difference in thin films due to transmitted light. 5 4) Obtain an expression for the fringe width in case of interference at a wedge-shaped film. 6 5) Obtain an expression for the diameter of bright and dark ring in Newton's rings by reflected light. 7 8 6) Obtain an expression for the diameter of bright and dark ring in Newton's rings by transmitted light. 9 7) Describe an experiment to determine the wavelength of monochromatic light by Newton's rings. 10 11 8) Explain the Principle, Construction and working of Michelson’s Interferometer. 12 9) Explain Circular fringes and straight fringes in Michelson Interferometer 13 14 15 10) Describe an experiment to determine the wavelength of monochromatic light by Michelson's Interferometer. 16 11) Mention the uses of Michelson Interferometer. 17 Ten Marks Questions 1) Describe with a neat diagram the Fresnel's biprism obtain an expression for fringe width with necessary theory. (KUD-2010) 18 2) Obtain the expression for total path difference of reflected and transmitted light from a thin film and hence obtain the condition for maxima and minima in these cases. (KUD-2011) Refer Question Numbers 2 & 3 3) What are Newton's rings? How are they formed? Obtain the expression for the radii of mth bright and dark rings due to reflected light. (KUD-2011) Refer Question Numbers 9(2M), (5 & 6) in 5Marks 4) Describe the construction and working of Michelson's interferometer. How it is used to determine the wavelength of monochromatic light. (KUD-2010, 2009, 2007) Refer Question Numbers 8 & 10 19 PROBLEMS: 20 21 22 23 24 25 26 27 28 29 30 PROBLEMS 1) A biprism is placed at distance of 5×10²m in front a narrow slit, illuminated by sodium light of wavelength 5890Aº and the distance between the virtual sources is found to be 0.05x10-2m. Find the width of the fringes observed in an eyepiece placed at a distance of 0.75m from the biprism. (Ans: 0.94x10m) 2) A thin sheet of a transparent material (n=1.60) is placed in the path of one of the interfering beams in a biprism experiment using sodium light, λ=5890Aº. The central fringe shifts to a position originally occupied by the 12th bright fringe calculate the thickness of the sheet. (Ans: t=0.12μm) 3) When a thin sheet of transparent material of thickness 6.3x10 m is introduced in the path of one of the interfering beams, the central fringe shifts to a position occupied by the sixth fringe. If λ=5460A°. Find the refractive index of the sheet. (Ans: n=1.52) 4) A parallel beam of light of wavelength 6x107m is incident on a thin glass plate (n=1.6) such that the angle of refraction into the plate is 45°, calculate the smallest thickness of the glass plate which will appear dark by reflection. (Ans: t=2.65x10-7m) 5) A glass wedge of angle 0.01 radian is illuminated by monochromatic light of 6000Aº falling normally on it. At what distance from the edge of the wedge, will be 10th fringe be observed by reflected light. (Ans: x=0.3x10-²m) 6) In a Newton's rings experiment the diameter of the 15th ring was found to be 0.620×102m and that of the 5th ring was 0.420×102m. If the radius of the plano-convex lens is 1.2m calculate the wavelength of light used. (Ans: A=4333Aº) 7) In a Newton's rings experiment, the diameter of the 10th ring was 0.45x10-2m and the diameter of the 20th ring is 0.704x102m. Find the radius of curvature of the plano-convex lens if the wavelength of light is 5890Aº. (Ans: R=1.2m) 8) A plano-convex lens of radius of 3m is placed on an optically flat glass and is illuminated by monochromatic light. The diameter of the 8th dark ring in the transmitted system is 0.72×102m. Calculate the wavelength of light used. 5760Aº) 9) In a Newton's rings experiment the diameter of the 15th ring was found to be 0.590cm and that of the 5th ring was 0.336cm. If the radius of the plano-convex lens is 100cm calculate the wavelength of light used. (Ans: λ=5880Aº) 10) In moving one mirror in a Michelson interferometer through a distance of 0.1474mm, 500 fringes cross the centre of the field of view. What is the wavelength of light ? .(Ans: λ=5896Aº) 31