I need the answer as soon as possible 3.8. Number of wave guide modes With increasing V

I need the answer as soon as possible

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3.8. Number of wave guide modes With increasing V parameter (3.18) not only the number of allowed values for Je(X) increases but also the num- ber of roots Xem <V continues to rise. In order to estimate the number of modes for a given V parameter, begin by assuring yourself that Je(x) ≈ (2/лx)¹/2 cos(x - (l+1/2)π/2) is a good approximation for large x. Use this approximation to calculate explicitly the number M of allowed modes and show that it rises with M 4V²/². Calculate the mode number for a step- index fibre with NA = 0.2 and core diameter 2a = 50 um. How does the mode number change if the cladding is replaced with air, i.e. if a pure solid 50 μm diameter glass fibre is used? 3.8. Number of wave guide modes With increasing V parameter (3.18) not only the number of allowed values for Je(X) increases but also the num- ber of roots Xem <V continues to rise. In order to estimate the number of modes for a given V parameter, begin by assuring yourself that Je(x) ≈ (2/лx)¹/2 cos(x - (l+1/2)π/2) is a good approximation for large x. Use this approximation to calculate explicitly the number M of allowed modes and show that it rises with M 4V²/². Calculate the mode number for a step- index fibre with NA = 0.2 and core diameter 2a = 50 um. How does the mode number change if the cladding is replaced with air, i.e. if a pure solid 50 μm diameter glass fibre is used?

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