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Chapter 30: Problem 6
In glass, which end of the visible spectrum has the smallest critical angle for total internal reflection?
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A scuba diver sets off a camera flash at depth \(h\) in water with refractive index \(n .\) Show that light emerges from the water's surface through a circle of diameter \(2 h / \sqrt{n^{2}-1}.\)
Why does a spoon appear bent when it's in a glass of water?
Show that a three-dimensional corner reflector (three mutually perpendicular mirrors, or a solid cube in which total internal reflection occurs) turns an incident light ray through \(180^{\circ} .\) (Hint: Let \(\vec{q}=q_{x} \hat{\imath}+q_{y} \hat{\jmath}+q_{z} \hat{k}\) be a vector in the propagation direction. How does this vector get changed on reflection by a mirror in a plane defined by two of the coordinate axes?)
Through what angle should you rotate a mirror so that a reflected ray rotates through \(30^{\circ} ?\)
You're standing \(2.3 \mathrm{m}\) horizontally from the edge of a 4.5 -m-deep lake, with your eyes \(1.7 \mathrm{m}\) above the water's surface. A diver holding a flashlight at the lake bottom shines the light so you can see it. If the light in the water makes a \(42^{\circ}\) angle with the vertical, at what horizontal distance is the diver from the edge of the lake?
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