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Furkat [3]
3 years ago
5

The index of refraction of quartz is anisotropic. Suppose that visible light is passing from one grain to another of different c

rystallographic orientation and at normal incidence to the grain boundary. Calculate the reflectivity at the boundary if the indices of refraction for the two grains are 1.544 and 1.553.
Mathematics
1 answer:
Anestetic [448]3 years ago
3 0

Answer:

The reflectivity at the boundary of the two grains is 2.9×{10}^{-3}

Step-by-step explanation:

Given :

Refractive index of one grains (n_{1}) = 1.553

Refractive index of second grains (n_{2}) = 1.544

According to the fresnel equation,

∴ general equation of refraction ( reflectivity ) r = \frac{ n_{1} cos\alpha _{i}  - n_{2}cos_{t} }{ n_{1} cos\alpha _{i}  + n_{2}cos_{t} }

where cos\alpha _{i} = incident angle, cos\alpha _{t} = transmitted angle

but for normal incidence \alpha = 0°

so our equation become,

⇒   r =  \frac{n_{1} - n_{2} }{n_{1} + n_{2}}

     r = \frac{1.553 - 1.544}{1.553 + 1.544}

     r = \frac{0.009}{3.097}

     r = 2.9×10^{-3}

Therefor reflectivity at the boundary is given by r = 2.9×10^{-3}.

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