The Crystal Ball Fortune Teller · AI Generator #GEN-01B83064

Physics · optics

Problem

A fortune teller uses a crystal ball made of glass with refractive index n=1.60n = 1.60 and radius R=8.0  cmR = 8.0\;\text{cm}. She places a small LED light source at distance d=12.0  cmd = 12.0\;\text{cm} from the center of the ball, creating mysterious glowing patterns inside. The LED emits unpolarized light at wavelength λ=650  nm\lambda = 650\;\text{nm} in vacuum. (a) What is the critical angle for total internal reflection at the glass-air interface? (b) Light rays from the LED enter the crystal ball and some undergo total internal reflection at the far surface. Find the minimum distance from the ball's center where the LED must be placed so that a ray passing through the center of the ball will just undergo total internal reflection at the exit point. (c) For the LED at its actual position (d=12.0  cmd = 12.0\;\text{cm}), consider a ray that enters the ball at the point closest to the LED and travels toward the center. At what angle (measured from the normal to the surface) does this ray strike the exit surface of the ball?

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