zoe asked in Science & MathematicsPhysics · 4 months ago

how do you calculate the critical angle for diamonds.?

physics help

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• 4 months ago

By snail's Law:-

=>n1sinθ1 = n2sinθ2=>n1sin90° = n2sin(θc) =>(1)(1) = n2sin(θc)   {assume n1 = 1.00 (air) }sin(θc) = 1/n

Since diamond has an index of refraction n = 2.42

=>sin(θc) = 1/n(diamond)

sin(θc) = 1/2.42

(θc) = 24.4°

The top facets of a diamond made with steep angle and the lower facets at such a shallow angle to have a ray of light entering vertically from above reflects within the diamond until it escapes out the top.

=>The idea is to readily admit and let light escape from the top θi < θc; θr < θc but have TIR at all surfaces below the top so light reflects within the diamond θi = θr> θc until it escapes out the top.

• 4 months ago

You look up the refractive index (n) of diamond.  It is n=2.417 ( https://en.wikipedia.org/wiki/List_of_refractive_i... )

Then use the formula: critical angle = sin⁻¹(1/n)

= sin⁻¹(1/2.417) = sin⁻¹(0.4137) = 24.4º