H26.6. Glass bottom boats are used to give passengers a spectacular view of natu

Question

H26.6. Glass bottom boats are used to give passengers a spectacular view of natural reefs and marine life. Given nair 1.0, nolass 1.6, nwoter 1.33. a) A light ray from a fish enters the glass at an incident-angle of-0-34. At what angle of refraction does the ray exit the glass into air? b) What is the critical angle for total internal reflection of light from glass to air? c) A light ray from a fish strikes the glass to air inter face at the critical angle. With what angle, Co, did the ray enter the glass from the water? At angles larger than this, light from the fish will not enter the boat. d) What is the critical angle for total internal reflection of light from glass to water? e) Prove that the reverse of part (c) is not possible. That is, there is no angle, 8o, for which a light ray from inside the boat will strike the glass to water interface at a critical angle. air 0% glass water 34°

Explanation / Answer

given nair = 1

nglass = 1.6

nwater = 1.33

a. let final angle of refracton = r

then

sin(34)/sin(r1) = ng/nw

sin(r)1)/sin(r) = na/ng

sin(34)/in(r) = na/nw

hence

r = 48.04 deg

b. for glass to air

critical angle of reflection = theta

sin(theta) = 1/1.33

theta = 48.753 deg

c. let angle of incidence be i

sin(i)/sin(48.753) = ng/nw = 1.6/1.33

i = 64.75 deg

d. from glass to water

sin(i)/sin(90) = nw/ng = 1.33/1.6

i = 56.227 deg

e. for glass to water interface angle of 56.227 deg

sin(i)/sin(56.227) = ng/na = 1/6

sin(i) = 1.3299

which is not possible

hence light from the boat can never reach glass water interface at critical angle

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