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 watersoluble.) He holds a powerful laser weapon y1 = 1.49 m above the surface of the water and fires at an angle of θ1 = 27◦ to the horizontal. He hits the Boy Wonder squarely on the letter "R", which is located y2 = 3.77 m below the surface of the water. θ x y y 1 1 2 R J Batplastic surface Mirrored Surface water B 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.

To solve this exercise we must work in parts. Let's use the law of refraction to find the angle of the refracted ray and trigonometry to find the distances.

Let's start by looking for the angles that the laser refracts

n₁ sin θ₁ = n₂ sin θ₂

where n₁ is the air refraction compensation n₁ = 1, n₂ the water refractive index n₂ = 1,333

θ₂ = sin⁻¹ (n₁ sin θ₁/n₂)

θ₂ = sin⁻¹ (1 sin 27 / 1,333)

θ₂ = sin⁻¹ 0.34057

θ₂ = 19.9º

now let's find the distance from the edge of the pool to the point where the ₂lightning strikes the water

tan θ₁ = y₁ / x₁

x₁ = y₁ / tan θ₁

x₁ = 1.49 / tan 27

x₁ = 2,924 m

Now let's look for the waterfall in the water as far as Robin

tan θ₂₂ = y₂ / x₂

x₂ = y₂ / tan θ₂

x₂ = 3.77 / tan 19.9

x₂ = 1,364

the distance from the edge of the pool to Robin is

x_total = x₁ + x₂

x_total = 2,924 + 1,364

x_total = 4.29m