Can you help me solve 1, 2, 3, 4, 5, 6, 7, 8 with fully explanation.
1. What are the three smallest thicknesses of a soap bubble capable of producing reflective destructive interference for light with a wavelength of 645 nm in air? (Assume that the index of refraction of soapy water is the same as that of pure water, 1.33.) 2. Athin layer of glass (n = 1.50) oats on a transparent liquid (n = 1.35). The glass is illuminated from above by light with a wavelength, in air, of 5.80 x 102 nm. Calculate the minimum thickness of the glass, in nanometres, other than zero. capable of producing destructive interference in the reflected light. Draw a diagram as part of your solution. 3. A coating, 177.4 nm thick, is applied to a lens to minimize reflections. The respective indexes of refraction of the coating and of the lens material are 1.55 and 1.48. What wavelength in air is minimally reected for normal incidence in the smallest thickness? Draw a diagram as part of your solution. 4. Atransparent oil (n = 1.29) spills onto the surface of water (n = 1.33), producing a maximum of reflection with normally incident orange light, with a wavelength of 6.00 X 10'F m in air. Assuming the maximum occurs in the first order. determine the thickness of the oil slick. Draw a diagram as part of your solution. 5. What is the minimum thickness of an air layer between two flat glass surfaces (a) if the glass is to appear bright when 4.50 X 102-nm light is incident at 90\"? (b) if the glass is to appear dark? Use a diagram to explain your reasoning in both cases. 6. Afilm of gasoline (n = 1.40) floats on water (n = 1.33). Yellow light, of wavelength 5.80 X 102 nm, shines on this film at an angle of 90" (a) Determine the minimum nonzero thickness of the film, such that the film appears bright yellow from constructive interference. (b) What would your answer have been if the gasoline had been spread over glass (n = 1.52) rather than over water? 7. Two plane glass plates 10.0 cm long, touching at one end, are separated at the other end by a strip of paper 1.5 x 10*\" mm thick. When the plates are illuminated by monochromatic light, the average distance between consecutive dark fringes is 0, 20 cm. Calculate the wavelength of the light. 8. Athin layer of glass (n = 1.50)oats on a transparent liquid (n = 1.35). The glass is illuminated by light with a wavelength of 580 nm, in air. Calculate the minimum thickness of the glass, otherthan zero, capable of producing destructive interference in the reflected light. (1.9 x 104-7 m)
