A point source of light is submerged 2.4 m below the surface of a lake and emits

Question

A point source of light is submerged 2.4 m below the surface of a lake and emits rays in all directions. On the surface of the lake, directly above the source, the area illuminated is a circle. What is the maximum radius that this circle could have? Additional Materials Section 263 . paints CJ10 26 P 033 The drawing shows a crystalline quartz slab with a rectangular cross section. A ray of light strikes the slab at an incident angle of ": 270, enters the quartz, and travels to point P. This slab is surrounded by a fluid with a refractive index n. What is the maximum value of n such that total internal reflection occurs at point P? (nquartz -1.544) Additional Materials LSecion 26.3 For light that originates within a liquid and strikes the liquid/air interface, the critical angle is 37. What is Brewster's angle for this light? Additional Materials Section 264 A ray of sunlight is passing from diamond into crown glass; the angle of incidence is 28.00°. The indices of refraction for the blue and red components of the ray are: blue (ndiamond = 2.444, ncrown glass = 1.531), and red (ndiamond -2.410, ncrown glass-1.520). Determine the angle between the refracted blue and red rays in the crown glass.

Explanation / Answer

at critical angle condition

nwater*sinC = nair*sin90

(4/3)*sinc = 1

c = 48.6 degrees

tanC = R/h

R = h*tanc = 2.4*tan48.6 = 2.72 m

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from snell law of refraction

n*sintheta1 = nquartz*sintheta2 ......(1)

at point P

for critical angel angel of refraction in fluid = 90

nquartz*sin(90-theta2) = n*sin90

nquartz*costheta2) = n*sin90.............(2)

from 1 & 2

tantheta2 = sintheta1

tantheta2 = sin27

theta2 = 24.4

n*sin27 = 1.544*sin24.4

n = 1.405 <<-------------ANSWER

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sinC = nair/nliquid

nliquid = sinC*nair = sinC*1

nliquid = sinC

tantheta_b = nliquid/nair

tan(theta_b) = sinC

brewsters angle = 31 degrees

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for blue rays

ndiamond*sini = ncrown*sinr1

2.444*sin28 = 1.531*sinr1

r1 = 48.54 degrees

for red rays

ndiamond*sini = ncrown*sinr2

2.41*sin28 = 1.52*sinr2

r2 = 48.1 degrees

angel between blue and red rays = r1 - r2 = 0.44 degrees

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