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- In the figure, a light wave along ray r, reflects once from a mirror and a light wave along ray r2 reflects twice from that same mirror and once from a tiny mirror at distance L from the bigger mirror. (Neglect the slight tilt of the rays.) The waves have wavelength 660 nm and are initially exactly out of phase. What are the (a) smallest, (b) second smallest, and (c) third smallest values of L that result in the final waves being exactly in phase? (a) Number i Units nm (b) Number Units nm (c) Number i Units nm2. A 50-cm tall fish tank is 3/4 full with oil and exposed to the air. A laser beam with a wavelength of 6333 Å (633.3 nm) is incident on the surface of the oil at an angle of 20° above the surface. (a) How far does the laser beam travel in the oil? (b) How long after striking the surface of the oil does it take for the laser beam to reach the bottom of the tank? Note- the index of refraction for the oil is 1.48. [Answer: (a) d = 0.49 m; (b) At = 2.4 × 10-9 s]4. Two coherent beams having parallel electric fields are described by TT E₁ = 5 cos(ks₁ · wt + 3) E₂ = 3 cos +7) (ks₂ - wt+ With amplitudes in kV/m. the beams interfere at a point P where the phase difference due to path is π/4. At the point of superposition, calculate the net irradiance.
- Prove that the degree of polarization (Vr) of reflected light can be expressed as: Vr = R⊥− R∥ / R⊥+ R∥10. An unpolarized beam of light passes through two polarizers with an angle 30° between their transmission axes. What is the ratio of intensity of the light transmitted through both polarizers to the intensity between the polarizers ? A 1:2 В 1:4 C 3:4 D 1:8Question A2 Red light of vacuum wavelength 650 nm is travelling in a non-magnetic dielectric glass of refrac- tive index ng = 1.60. Calculate the impedance of the glass, the wavelength of light in the glass, and the critical angle 0c for total internal reflection at a glass-air interface. Question A3 Light is incident from air onto a horizontal surface of water of refractive index nw = 1.33. Calculate the Brewster angle at which the reflectance for the TM polarisation is zero. Also, cal- culate the power reflection coefficient RTE for TE-polarised light incident at this Brewster angle.
- Identify the direction of wave-propagation by calculating Poynting Vector for following waves: i. E = te-jßz; Ĥ = îne-jßz ii. Ē = telBz, Ĥ = -ŷnelßz iii. Ē = î sin ß,z; Ħ = -ŷ z cos B,z %3D jwu1. A 10 mW beam propagates in a medium with n = 1.5+ (5 × 10-4) i and has a vacuum wavelength of 750 nm. What is the wavelength in the material and how far does it go into the material before its power is reduced to 1 mW?8. Three polarizing disks whose planes are parallel and centered on common axıs. The directions of their transmission axes relative to the vertical are respectively: 0 = 17°, 6, = 42°, and 0, 75°. A beam of light polarized along the vertical is incident onto the first polarizer with an intensity of 1o = 20 W/m2, Calculate the transmitted intensity through all three polarizers. W/m2
- If I have a light with a frequency of 5 x 10^14 what is the wave length in nm?3. Electromagnetic waves from a radio station pass through an open window of a house. The square window has side length 0.75 m and the waves pass through perpendicular to the window's area. The electric field is measured at the window and found to be 0.02 V/m. In air, we can use the vacuum permeability = 4 x 10-7 H/m. (i) What is the magnitude of the Poynting vector, S, for the radio waves passing through the window? (ii) How much energy do the radio waves carry through the window during a 2-minute-long broadcast of BBC Radio 4's shipping forecast? [Hint: think of the units of S [units = (J/s)/m²] and Energy [units = J].4