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 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.

Answer 1

Answer:

 x_total = 4.29m

 

Explanation:

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