Hi, Im stuck with a waves question and could really usesome advice, the question

Question

Hi, Im stuck with a waves question and could really usesome advice, the question is as follows: "we wish to use a 45-45-90 degree prism to totallyinternally reflect light. what is the minimum refractive index thatthe glass must have in order for this to work? If this minimum refractive index corresponds to therefractive index of the glass for blue light, will red light alsobe totally internally reflected? why?" My working: Critical angle of glass = 43 refractive index of air = 1 sin 43 = (n2/n1) n1 = 1/sin 43 n1 = 1.466 I have a funny feeling this is wrong but other then this wayof working im not sure where to go. as for the second part of thequestion im completely boggled. im assuming the bigger wavelengthof red light has some impact on it but not sure where that comesinto it either. can someone point me in the right direction? thanks in advance Jase Hi, Im stuck with a waves question and could really usesome advice, the question is as follows: "we wish to use a 45-45-90 degree prism to totallyinternally reflect light. what is the minimum refractive index thatthe glass must have in order for this to work? If this minimum refractive index corresponds to therefractive index of the glass for blue light, will red light alsobe totally internally reflected? why?" My working: Critical angle of glass = 43 refractive index of air = 1 sin 43 = (n2/n1) n1 = 1/sin 43 n1 = 1.466 I have a funny feeling this is wrong but other then this wayof working im not sure where to go. as for the second part of thequestion im completely boggled. im assuming the bigger wavelengthof red light has some impact on it but not sure where that comesinto it either. can someone point me in the right direction? thanks in advance Jase I have a funny feeling this is wrong but other then this wayof working im not sure where to go. as for the second part of thequestion im completely boggled. im assuming the bigger wavelengthof red light has some impact on it but not sure where that comesinto it either. can someone point me in the right direction? thanks in advance Jase

Explanation / Answer

The critical angle is the angle of incidence above which totalinternal reflection occurs. The angle of incidence is measured withrespect to the normal at the refractive boundary. The criticalangle c is given by: c =sin-1(n2/n1) ----------(1) where n2 is the refractive index of the lessoptically dense medium,and n1 is the refractive index ofthe more optically dense medium. n2 refractive index of air and has a value 1 n1 is the refractive index of glass the critical angle is c = 45o or sin(45o) = (n2/n1) or n1 = (n2/sin(45o)) =(1/(1/2)) = 2 = 1.414 the wavelength of red light is = 700 nm = 700 *10-9 m the refractive index is given by n = (c/v) According to De Broglie's theory we have = (h/m * v) or v = (h/m * ) or n = (c/(h/m * )) = (c * m * /h)-----------(2) c = 3 * 108 m/s m = 9.1 * 10-31 kg h = 6.63 * 10-34 J-s from equation (2) the refarctive index of red light is largewhen compared to blue light as the wavelength of red colour islarge. From equation (1) we get the value of sinc assmall therefore the critical angle for red colour is reduced by45o and hence the light will not be totally internallyreflected. or sin(45o) = (n2/n1) or n1 = (n2/sin(45o)) =(1/(1/2)) = 2 = 1.414 the wavelength of red light is = 700 nm = 700 *10-9 m the refractive index is given by n = (c/v) According to De Broglie's theory we have = (h/m * v) or v = (h/m * ) or n = (c/(h/m * )) = (c * m * /h)-----------(2) c = 3 * 108 m/s m = 9.1 * 10-31 kg h = 6.63 * 10-34 J-s from equation (2) the refarctive index of red light is largewhen compared to blue light as the wavelength of red colour islarge. From equation (1) we get the value of sinc assmall therefore the critical angle for red colour is reduced by45o and hence the light will not be totally internallyreflected.

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