White light is incident normally on a diffraction grating with 300 lines/mm. The resulting diffracted light is then focused via a lens of focal length ƒ = +75 mm onto a detector. The lens and detector are aligned so that the first-order diffracted light at 550 nm is co-axial with the lens and focuses onto the centre of the detector. The hydrogen atom can emit two spectral lines (called Ha, Hẞ) at respective wavelengths 656 nm and 486 nm. Calculate the separation on the detector between the first-order diffracted light of these latter two wavelengths.
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- A ray of light is incident on an air/water interface. The ray makes an angle of θ1 = 34 degrees with respect to the normal of the surface. The index of the air is n1 = 1 while water is n2 = 1.33. Part (a) Numerically, what is the angle in degrees? θ2 =? Part (b) Write an expression for the reflection angle ψ, with respect to the surface. ψ =? Part (c) Numerically, what is this angle in degrees? ψ =?An x-ray beam of a certain wavelength is incident on a NaCl crystal, at 24.0° to a certain family of reflecting planes of spacing 39.8 pm. If the reflection from those planes is of the first order, what is the wavelength of the x rays?A certain device for analyzing electromagnetic radiation is based on the Bragg scattering of the radiation from a crystal. For radiation of wavelength 0.149 nm, the first-order Bragg peak appears centered at an angle of 15.15°. The aperture of the analyzer passes radiation in the angular range of 0.015°. What is the corresponding range of wavelengths passing through the analyzer?
- Often in optics scientists take advantage of effects that require very high intensity light. To get the desired effect a scientist uses a laser with power P = 0.0065 W to reach an intensity of I = 170 W/cm2 by focusing it through a lens of focal length f = 0.11 m. The beam has a radius of r = 0.0011m when it enters the lens. Randomized VariablesP = 0.0065 WI = 170 W/cm2f = 0.11 mr = 0.0011 Part (a) Express the radius of the beam, rp, at the point where it reaches the desired intensity in terms of the given quantities. (In other words, what radius does the beam have to have after passing through the lens in order to have the desired intensity?) Part (b) Give an expression for the tangent of the angle that the edge of the beam exits the lens with with respect to the normal to the lens surface, in terms of r and f? Part (c) Express the distance, D, between the lens's focal point and the illuminated object using tan(α) and rp. Part (d) Find the distance, D, in centimeters.…In the configuration shown in the figure, how much flux in watts falls on a 1-mm x 1-mm detector that is placed on-axis in the image plane? The source is 2 cm x 2 cm, Lambertian, with radiance 5 W/cm²-sr. The object distance, p, is 50 cm; the image distance, q, is 25 cm. The lens diameter is 5 cm. Neglect diffraction effects and Fresnel losses. source P Figure P2.2 9 detThe plane z = 0 separates two media: glass(nglass = 1.51 for z < 0) and water (nH20 = 1.33 for z > 0). The optical beam of a helium-cadmium (He-Cd) laser has a wavelength in vacuum of 325 nm. Consider that the laser beam propagates in the x-z plane from the glass side towards the glass/water interface at an angle of incidence of 30° (angle between the incident beam and the normal to the interface). Determine the Cartesian components of the k-vector (kx, ky, kz) for the incident reflected, and transmitted beams.
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