Batman and Robin are attempting to escape that dastardly villain, the Joker, by

Question

Batman and Robin are attempting to escape that dastardly villain, the Joker, by hiding in a large pool of water (refractive index nwater = 1.333). The Joker stands gloating at the edge of the pool. (His makeup is water-soluble.) He holds a powerful laser weapon y1 = 1.23 m above the surface of the water and fires at an angle of ?1 = 29.8 ? to the horizontal. He hits the Boy Wonder squarely on the letter “R”, which is located y2 = 4.2 m below the surface of the water.

Batman attempts to hide out in a Batbox. The top is a mirrored surface, but the vertical sides are made of clear Batplastic (refractive index np = 1.333). It is located x = 2.76 m horizontally from the edge of the pool. What is the minimum depth (measured to the top of the Batbox) that the Batbox can be below the surface of the water for the Caped Crusader to remain hidden from the Joker? Assume: The Joker gets down close to the water for the best view. Answer in units of m.

Explanation / Answer

a)

by using snells law

1 * sin( 90 - 29.8 ) = 1.33 * sin(x)

sin^-1( sin60.2 / 1.33) = x

x = 40.73 deg

then

1.23 / tan(29.8) = x

x = 2.148

then

4.2 * tan( 90 - 40.73) = 4.878

so the robin from edge of the pool is = 4.878 + 2.148 = 7.026 m

b)

by using snells law

x = 2.76 m

tan(90deg - 4.73deg) * 2.76 = 3.2 m

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