Please answer 22 Highlighted Portion. Batman and Robin arc attempting to escape

Question

Please answer 22 Highlighted Portion.

Batman and Robin arc attempting to escape that dastardly villain, the Joker, by hiding in a large pool of water (refractive index n water =1.333). The Joker stands gloating at the edge of the pool. (His makeup Is water-soluble.) He holds a powerful laser weapon y1 = 1.17 m above the surface of the water and fires at an angle of theta = 29.8 degree to the horizontal. He hits the Boy Wonder squarely on the letter "R", which is located y2 = 4.25 m below the surface of the water. How far (horizontal distance) is Robin from the edge of the pool? (Fear not. Batfans. The "R" is made of laser-reflective material.) Answer in units of m Batman attempts to hide out in a Bat box. The top is a mirrored surface, but the vertical sides are made of clear Bat plastic (refractive index np = 1.333). It is located.x = 3.47 m horizontally from the edge of the pool. What is the minimum depth (measured to the top of the Batbox) that the Bat box 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 in

Explanation / Answer

Angle of incidence i =29.8
angle of refraction = sinr
from snells law
sini/sinr = v1/v2 = u2/u1 = 1.333/1
sinr = sini/1.333 = .37
r = 21.8 degrees
given y2 = 4.25 mt

from robin positioned triangle
tan = distance of robin fom incidident/y2

tan(90-21.8) = x/4.25

x = 10.6 mt

from angle of incidence

tan29.8 = y1/y

y = 1.17/.57 = 2.05 mt

so horizontal ditance of robin = 10.6+2.05 = 12.65m

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