a scuba diver in a pool looks at his instructor. the angle between the ray in the water and the perpendicular to the water is 25. find the height of the instructors head

   y= y'  0.67

Explanation:

This is an exercise in refraction of light,

         n₁ sin θ₁ = n₂ sin θ₂

where subscript 1 is used for the incident medium and subscript 2 for the refracted medium

          sin θ₁ = n2 /n1   sin θ₂

the incident medium is air with refractive index n1 = 1 and the medium where the ray is refracted is water with n = 1.33

        let's calculate

        sin θ₁ = 1.33 / 1 sin  25

        θ₁ = sin⁻¹ (0.56208)

        θ₁ = 34.2º

when the ray is refracted we can assume that the adjacent leg (water surface) is the same for the two media

let's use the trigonometry relationship

          tan θ₁ = x / y

          tan θ₂ = x / y '

         tan θ₁ = y’ tan θ₂

         y = y ’ tanθ₂ / tan θ₁

to finish exercise you must know the depth of the object

         y =y'  tan 25/ tan 34.2

         y= y'  0.67

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards