a)If the incident angle from the air is 30 degrees and the refracted angle withi

Question

a)If the incident angle from the air is 30 degrees and the refracted angle within the glass in 20 degrees what is the index of refraction of the glass plate?

b)What is the critical angle for light coming up through the glass towards the air?

c) What is the Brewster angle for light incident upon the glass towards the air?

d)Tha above glass plate is sitting on top of a drawing of a mermaid. IF the glass plate is 2.44 cm thick, what is the apparent depth of the mermaid?

Please help and provide brief explanation so I can understand this better!

Explanation / Answer

na sin theta = ng sin phi      na = index of refraction of air = 1, and ng = index of refraction of glass

theta = angle of incidence and phi = angle of refraction

a) ng = 1 * sin 30 / sin 20 = 1.46      index of refraction of glass

b)   1.46 sin theta = 1 * sin 90        angle of refraction = 90 (no light transmitted - complete reflection)

sin theta = 1 / 1.46 = .684    and theta = 43.2 deg      the critical angle

c) The Brewster angle occurs when the incident and refracted rays are at 90 deg to each other.

ng sin theta = sin phi       Snell's Law

ng = sin phi / sin theta      theta is the incident angle (within the glass)

phi + theta = 90       condition for Brewster's angle

theta = 90 - phi    Then

ng = sin phi / cos phi = tan phi = 1.46

phi = 55.6 deg    which is the angle of incidence within the glass (towards the air)

d) Apparent depth = depth / ng = 2.44 / 1.46 = 1.67 cm

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