given a GRIN slab of refraction index n(y)=n_0(1-1/2 α^2 y^2) and length d, show that the elements of the ABCD matrix are: A=cos(αd) B= 1/α sin(αd) C= -α sin(αd) D= cos (αd)

Q: Consider R=A+B+D, which of the following is correct? O Rx Ay+By+ Dy O tane=Ry/Rx OR=√(R₂)² + (R₂)²…

A:

Q: A beam of neutrons (of mass 940 MeV/c² ) moves through a material whose refractive index is 1.3.…

A: Given data, Mass of neutron M=940 MeV/c2. Refractive index n = 1.3 Angle cosθ=150.

Q: Show that if f(x) = Ac* where A and k are real constants, then f(x) satisfies: %3D d² f(x) + k° f(x)…

A:

Q: 1 using the Convolution The- Find the inverse Fourier transform of (iw + 3)3 (-) orem on Fourier…

A: I have written the formula for part of question in which we apply convolution theorem. Have a look

Q: Consider a He-Ne laser cavity consisting of two mirrors of reflectivities RỊ 1 and R2 = 0.98. The…

A:

Q: Find the fourier transform of f(x) defined by f(x) = { = ( and hence evaluate +∞ sin pacos pl du |x|

A:

Q: A standing wave of light in glass (index of refraction = 1.5) is observed to have a %3D distance of…

A:

Q: Find the Jones vector which represents a state of polarization orthogonal to E1 -2i,

A: Given Data E1=1-2i Now here we have find the jones vector E→2. which is orthogonal to E→1, Two…

Q: Let C be a black circular disk in front of a white background. The circular disk is parallel to the…

A: What would be the shape of the disk’s projection on the image plane ?

Q: = State Fermat's principle governing the paths traced by light rays in a medium. A horizontally…

A:

Q: A vector function is given as A = x(x-4) ey/6 cos(zπ/2) What is the result of f(V-A) dv over the…

A: Given that, the vector is  A→=x^x-4ey/6coszπ2 And the rectangular prism is   To find the value of…

Q: Polarizers can be made based on the principle of Brewster angle. In Fig. 2, a light ray (with 50%…

A: Answer:-  Given  Refractive index (n1) = 1.33  Refractive index (n2) = 1.5  Refractive index (n3) =…

Q: A thick piece of Lucite (n = 1.50) has the shape of a quarter circle of radius R = 12.8 cm as shown…

A:

Q: In an experiment, the optical behaviour of a material was studied. The intensity of light, I,…

A:

Q: Compute the index of refraction for the substance where lightpropagates with speed v = 2.4 × 10 8…

A: Refractive index defined as the ratio of speed of light in vaccum to the velocity of light in the…

Q: Light from a source A at (-1,1) is reflected by a plane mirror placed along the x-axis to a receiver…

A: The distance between two points x1,y1 and x2,y2 is given by the formula, d=y2-y12+x2-x12 To find the…

Q: Most real time clock chips use 32.678 KHz crystals (2^15), Why clock chips of 2^12 Hz or 2^18 Hz are…

A: The frequency of a real time clock varies with the application. The frequency 32.768 KHz is commonly…

Q: An airplane is above a straight road on which are two observers 1640 m apart. At a given signal the…

A: Given Data : The distance between the two observers is given as d = 1640 m. The angle observed by…

Q: Let x(t) = [4 cos(100t) + sin(100t) + e-50t cos(50/19t)]. Then deduce that 2 85 (a) x(t) solves (t)…

A:

Q: sider a typical red laser pointer with wavelength 649 nm. What is the light's frequency in hertz?…

A: Wavelength of red laser light is λ=649×10-9 m Speed of light is c=3×108 m/s

Q: Line l passes through the points (7,6) and (4,0). Write the equation of the image of l after a…

A: For the given points first, we need  to find the equation of the line and slope of the line  as the…

Q: 6.38. A coaxial line of inner and outer radii a and b, respectively, is mounted on an infinite…

A: In the far zone, the E and H field components are orthogonal to each other and form TEM mode fields.…

Q: A thick lens consists of two spherical surfaces with curvature R₁, R₂ separated by a thickness d of…

A: We want to find the power of a thick lens consisting of two spherical surfaces with curvatures R1…

Q: The explanation given in your textbook for the color of the setting Sun should apply equally well to…

A: sunsets are redder than sunrises. Why?

Q: sin (a) ji(x) = (b) ja(=) = (흙-1) sin z (c) n(x) =D -프 COS I %3D sin z - cos z 3 COS I sin I

A:

Q: The Fourier transform of a function f (x) is defined as: f (w) = L dx f (ω) -. f (x)e-iwx Similarly,…

A: Given,  Fourier transform formula and inverse Fourier transform formula  And the function f(x) .

Q: Given the Dispersion relation n=1+2pi*(B/wavelength) where B is 10nm, find the group and phase…

A:

Q: Two vectors A and B are perpendicular to one another. Which of the following statements is true? O A…

A:

Q: Compute the index of refraction for the substance where lightpropagates with speed v = 1.4 × 10 8…

A:

Q: For the transformation Q = /2g e-1+2a cos p, P = /2g e-a-1 sinp (where a is a constant) to be…

A: To be determined: For the canonical transformation, the value of alpha.

Q: A glass plate of thickness t and refractive index n is to be placed in a convergent beam normally.…

A:

Q: Compute the index of refraction for the substance where lightpropagates with speed V=1.1*10^ 8 m/s…

A: Answer:-  Given  Speed of light in medium (V) = 1.1 × 108 m/s  Speed of light in vacuum (C) = 3 ×…

Q: (a) The index of refraction for violet light in silica flint glass is 1.66, and that for red light…

A:

Q: A ray of light is incident on an air/water interface. The ray makes an angle of θ1 = 34 degrees with…

A: Given data The angle of incident is θ1=34o The refractive index of the air is n1=1 The refractive…

Q: Ray 1 of light in medium a (see (Figure 1)) strikes the surface at 51.0∘ with respect to the normal.…

A: *   Snell's  Law            n1sinθ1= n2sinθ2Given:                n1= 1.35                n2= 1.65…

Q: In the ray diagram of the figure, where the angles are not drawn to scale, the ray is incident at…

A: Given : Angle ø = 61.8o n1 = 1.74 and n2 = 1.60 Incident angle between medium 1 and medium 2 is at…

Q: Superimpose on a single plot EN, ER, and EA versus r up to 1.0 nm

A: Superimpose on a single plot EN, ER, and EA versus r up to 1.0 nm.

Q: Derive the Law of Reflection, ui = ur, by using the cal

A: Fermat's Principle: According to the This principle it is directed that the light will always pursue…

Q: A light of wavelength 4051 Å is incident normally on a glass slab of thickness 5 cm and R.I. 1.6.…

A: To find-Distance of source from incident surfaceGiven-Thickness of glass slab=d=5 cmμ=1.6λ=4051…

Q: Compute the index of refraction for the substance where light proper dates with speed V = 2.4•10^8…

A: A substance,  Speed of light in the material, v = 2.4 X 108 m/s Speed of light in vacuum, c = 3 X…

Q: Question 3: using 3D composite transformations, find out the reflection of the triangle given by the…

A: Rewriting all the triangle points in 4D column matrix, so that the translation can be done, xyz1…

Q: Prove that the angles of polarization (θp, θ'p) for internal and external reflection on the…

A: we have to prove θp+θ'p=90°

Q: An SPEC image is taken with a field of view (FOV) of 40 cm (in the x-direction). The image is…

A: (a) pixel size 1) 40cm*1pixel/128pixel = 40/128 = 0.31 2) 40cm* 1pixel /256pixel =40/256 = 0.156 3)…

Q: compute the index of refraction for the substance where lightpropagates with speed v=2.7 • 10^8 m/s.…

A: Refractive index is the ratio of the speed of light in vacuum to the speed of the light in that…

Q: Why were you not able to calculate ∠i ÷ ∠R or (sin ∠i ) ÷ (sin ∠R) for an angle of incidence of 0°?

A: