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Problem: The refractive index of silica versus wavelength can be described using: Where A1 = 0.696749, A2 = 0.408218, A3 = 0.890815, λ1 = 0.0690660 µm, λ2 = 0.115662 µm, λ3 = 9.900559 µm(a) Consider the case of oblique incidence from air to silica. If the incident light is in air and its incidence angle is θi = 89°, calculate the transmission angle θt if the optical wavelength in air is 400 nm, 600 nm, and 1.5 µm(b) An optical beam encounters a right triangle made of silica as shown in (a) in normal incidence configuration. The input power is Pi = 10 mW. Determine the output beam power P0. Perform the calculation at three different wavelengths as above.

FREE Expert Solution

From Snell's law:

ηisinθi=ηtsinθt

(a)

Refractive index at λ = 400 nm = 0.4 μm

η=1+(0.696749)(0.420.42-0.06906602)+(0.408218)(0.420.42-0.1156622)+(0.890815)(0.420.42-9.9005592)

η = 1.47

From Snell's law:

θt=sin-1[nisinθiηt]=sin-1[(1)sin(89°)1.47]

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Problem Details

The refractive index of silica versus wavelength can be described using: 

Where A1 = 0.696749, A2 = 0.408218, A3 = 0.890815, λ1 = 0.0690660 µm, λ2 = 0.115662 µm, λ3 = 9.900559 µm

(a) Consider the case of oblique incidence from air to silica. If the incident light is in air and its incidence angle is θi = 89°, calculate the transmission angle θt if the optical wavelength in air is 400 nm, 600 nm, and 1.5 µm

(b) An optical beam encounters a right triangle made of silica as shown in (a) in normal incidence configuration. The input power is Pi = 10 mW. Determine the output beam power P0. Perform the calculation at three different wavelengths as above.

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