# How Lighthouses Work 1, Exercise 1: the inverse square law
# A light of 250,000 candela (an assumed, illustrative figure). Find the
# illuminance it gives at 1, 2, 3 and 5 km, the distance at which it has fallen
# to 0.01 lx, and the intensity needed to give the same 0.01 lx at twice that
# distance.
import math

I = 250_000                          # assumed intensity, candela (illustrative)

def lux(i, d_m):
    return i / d_m ** 2

for km in (1, 2, 3, 5):
    print(f"{km} km", round(lux(I, km * 1000), 4))

# distance at which the light has fallen to 0.01 lx
d = math.sqrt(I / 0.01)
print(round(d), "m")

# intensity needed to give the same 0.01 lx at twice that distance
needed = 0.01 * (2 * d) ** 2
print(round(needed), round(needed / I, 1))

# Output when run:
# 1 km 0.25
# 2 km 0.0625
# 3 km 0.0278
# 5 km 0.01
# 5000 m
# 1000000 4.0
#
# Reading the output: 1 km gives 0.25 lx, and doubling to 2 km gives 0.0625 lx,
# a quarter. At 5 km the light has fallen to exactly 0.01 lx (5,000 m). To get
# the same 0.01 lx at 10 km the light would need 1,000,000 cd, which is 4.0
# times the intensity: doubling a distance costs four times the intensity.
# Note this ignores the haze in the air, which Allard's law (in the chapter)
# adds.