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# What is the smallest incident angle necessary to obtain total reflection from the XY interface?

When light travels from medium X to medium Y, the incident angle and refracted angle are 29 degrees and 42 degrees respectively. What is the smallest incident angle necessary to obtain total reflection from the XY interface?

Can someone also explain this concept a bit? Thank you!

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- jacob sLv 71 month ago
Apply smells law to light at interface of two mediums.

nxsini=nysinr

sini/sinr = ny/nx

ny/nx=sin29/sin42

ny/nx=0.724

The angle of refraction is 90 degrees if the light ray incident with critical angle .

Apply Snell's law to the light interface of two medium.

nxsinθc = nysin90

sinθc=(0.724)sin90

θc= sin^-1(0.724)

θc= 46.4 degrees

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