1. Calculate the resolving power of a Fabry-Perot interferometer
made of reflecting surfaces of reflectivity 0.85 and separated by a
distance 1 mm at λ = 4880 Å. Get solution
2. Calculate the minimum spacing between the plates of a Fabry-Perot interferometer which would resolve two lines with Δλ = 0.1 Å at λ = 6000 Å. Assume the reflectivity to be 0.8. Get solution
3. Consider a monochromatic beam of wavelength 6000 Å incident (from am extended source) on a Fabry-Perot etalon with n2 = 1, h = 1 cm and F = 200. Concentric rings are observed on the focal plane of a lens of focal length 20 cm(a) Calculate the reflectivity of each mirror.(b) Calculate the radii of the first four bright rings. What will be the corresponding value of m?(c) Calculate the angular width of each ring where the intensity falls by half and the corresponding FWHM (in mm) of each ring. Get solution
4. Consider now two wavelengths 6000 Å and 5999.9 Å incident on a Fabry-Perot etalon with the same parameters as given in the previous problem. Calculate the radii of the first three bright rings corresponding to each wavelength. What will be the corresponding values of m? Will the lines be resolved? Get solution
5. Consider a monochromatic beam of wavelength 6000 Å incident normally on a scanning Fabry-Perot interferometer with n2 = 1 and F = 400. The distance between the two mirrors is written as h = h0 + x. With h0 = 10 cm, calculate(a) The first three values of x for which we will have unit transmittivity and the corresponding value of m.(b) Also calculate the FWHM Δh for which the transmittivity will be half.(c) What would be the value of Δh if F was 200?[Ans: (a) x ≈ 200 nm (m = 333334),500 nm(m = 333335); (b) Δh ≈ 8 nm]. Get solution
6. In continuation of Problem16.5, consider now two wavelengths λ0 (= 6000 Å) and λ0 + Δλ incident normally on the Fabry-Perot interferometer with n2 = 1, F = 400 and h0 = 10 cm. What will be the value of Δλ so that T = ½ occurs at the same value of h for both the wavelengths.... Get solution
7. Consider a laser beam incident normally on the Fabry-Perot interferometer as shown in Fig 16.15.(a) Assume h0 = 0.1 m, c = 3 x 108 m/s, ν = ν0 = 5 x 1014 s-1. Plot T as a function of x (–100 nm x F = 200 and F = 1000.(b) Show that if ν = (ν0 ± p 1500 MHz; p = 1,2,…) we will have the same T vs. x curve; 1500 MHz isknown as the free spectral range (FSR). What will be the corresponding values of δ? Get solution
2. Calculate the minimum spacing between the plates of a Fabry-Perot interferometer which would resolve two lines with Δλ = 0.1 Å at λ = 6000 Å. Assume the reflectivity to be 0.8. Get solution
3. Consider a monochromatic beam of wavelength 6000 Å incident (from am extended source) on a Fabry-Perot etalon with n2 = 1, h = 1 cm and F = 200. Concentric rings are observed on the focal plane of a lens of focal length 20 cm(a) Calculate the reflectivity of each mirror.(b) Calculate the radii of the first four bright rings. What will be the corresponding value of m?(c) Calculate the angular width of each ring where the intensity falls by half and the corresponding FWHM (in mm) of each ring. Get solution
4. Consider now two wavelengths 6000 Å and 5999.9 Å incident on a Fabry-Perot etalon with the same parameters as given in the previous problem. Calculate the radii of the first three bright rings corresponding to each wavelength. What will be the corresponding values of m? Will the lines be resolved? Get solution
5. Consider a monochromatic beam of wavelength 6000 Å incident normally on a scanning Fabry-Perot interferometer with n2 = 1 and F = 400. The distance between the two mirrors is written as h = h0 + x. With h0 = 10 cm, calculate(a) The first three values of x for which we will have unit transmittivity and the corresponding value of m.(b) Also calculate the FWHM Δh for which the transmittivity will be half.(c) What would be the value of Δh if F was 200?[Ans: (a) x ≈ 200 nm (m = 333334),500 nm(m = 333335); (b) Δh ≈ 8 nm]. Get solution
6. In continuation of Problem16.5, consider now two wavelengths λ0 (= 6000 Å) and λ0 + Δλ incident normally on the Fabry-Perot interferometer with n2 = 1, F = 400 and h0 = 10 cm. What will be the value of Δλ so that T = ½ occurs at the same value of h for both the wavelengths.... Get solution
7. Consider a laser beam incident normally on the Fabry-Perot interferometer as shown in Fig 16.15.(a) Assume h0 = 0.1 m, c = 3 x 108 m/s, ν = ν0 = 5 x 1014 s-1. Plot T as a function of x (–100 nm x F = 200 and F = 1000.(b) Show that if ν = (ν0 ± p 1500 MHz; p = 1,2,…) we will have the same T vs. x curve; 1500 MHz isknown as the free spectral range (FSR). What will be the corresponding values of δ? Get solution
