Answer
Given,
Periscope uses 45-45-90 prisms with total internal reflection adjacent to 45°.
refractive index of water, n_a = 1.33
refractive index of glass, n_g = 1.52
When the light enters the water, water will act as a lens and when we see the object from the periscope the object shown is farther than the usual distance.
Answer:
Part a)

Part b)

Part c)

Part d)

Explanation:
Part a)
As we know that speed of package is same as that of helicopter in horizontal direction
So after time "t" the velocity in x direction will remain constant while in Y direction it will go free fall
So we have



Part b)
Distance from helicopter is same as the distance of free fall
so we will have

Part c)
If helicopter is rising upwards with uniform speed
then final speed of the package after time t is given as


Part d)
distance from helicopter

The angle of refraction would be further less
Refer to the diagram shown below.
v = the tangential speed.
r = the radius of the horizontal circle.
T = tension in the string.
θ = the angle that the string makes with the vertical
m = Bob's mass (mg = the weight)
F = centripetal force
l = the length of the string
From geometry,
r = l sin θ
The centripetal acceleration is

The centripetal force is

For vertical force balance,
T cosθ = mg (1)
For horizontal force balance,

(2)
Divide (2) by (1).

Answer: