The diagram (figure b) shows an acrylic semicircle with an incident laser beam b

Question

The diagram (figure b) shows an acrylic semicircle with an incident laser beam being reflected to point E and refracted to point C. The incident beam passes over the point D = 0.00 degree, and the line NN' (the normal to the flat surface) passes through 25.0 degree and 205 degree. (i) The index of refraction for this material is 1.64. Please find the angular position for the point E. (ii) Calculate the angular position of point C. (iii) What is the velocity of the light in the acrylic semicircle? (iv) What is the critical angle for total internal reflection for this substance? (v) When a semicircular transparent plate has its straight edge aligned with AA', as shown in Figure (a) the refracted beam is observed to disappear. If point B in Figure (a), is at 55.0 degree, determine the position of point R on the Ray Table. Please write couple of statements to support all of your answers. Recall that c = 3.00 times 10^8 m/s.

Explanation / Answer

For reflection, angle of incidence = angle of reflection.

So E is 25 + 25 = 50 degrees angular position from D

For refraction,

sin(i) = mu * sin (r) where mu = relative refractive index

So sin(25) = 1.64 * sin(r)

r = 14.93 degrees

= 205 - 14.93 = 190.07 degrees

Velocity of light = v/ mu = 3*10^8 / 1.64 m/s

Critical angle = i = asin(1/1.64) = 37.57 degrees

v) This is because, The angle of incidence is normal at the surface, So it passes right through without refraction, Gets reflected at straight edge from centre, and comes out without getting refracted.

If B = 55degrees from A'

then R = 180 - 55 = 125 degrees from A'

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