Question

In the diagram below, a light ray traveling in the vertical direction enters a circular piece of glass, travels a distance L = 160 mm through the glass, and then exits the glass. The distance from the original path of the light to a parallel line that passes through the center of the circle is d = 70.0 mm, and the total deviation of the light is 36.0O . Find the radius of the circle and the index of refraction of the glass.

d

Answer 1

"Let 0 be the center. 00' and 00"" be the normal on surfaces. Let angle of incidence = s angle of refraction = r (for Ist refraction) Let theta and theta' be deviation at respective refraction then, theta = j - r, and also, theta' = j - r theta = 0' and total deviation = theta + theta' = 36 degree theta = 18 degree because L - sin j = mu sin r sin (r + 18 degree) = mu sin r cos (r) = 160/2/ = 80/R also, R sin (r + theta) = d = 70 R sin j = 70 sin j/cos sr times 80 = 70 sin I = 7/8 cos r = 7/8 cos (j - 18) sin j = 7/8 {cos j cos (18) + sin (s) sin 18 degree} \r\n \sin j = 7/8 {0.95 cos I + 0.35 sin j} tan (j) = 0.27 tan j + 0.83 [dividing by cos j]"