Answer:
15.1 m
Explanation:
We first calculate the apparent depth from
refractive index, n = real depth/apparent depth
apparent depth, a = real depth/refractive index
real depth = 2.0 m, refractive index = 1.4
apparent depth, a = 2.0/1.4 = 1.43 m
Since the cylindrical cistern has a diameter of 2.9 m, its radius is 2.9/2 = 1.45 m
The angle of refraction, r is thus gotten from the ratio
tan r = radius/apparent depth = 1.45/1.43 = 1.014
r = tan⁻¹(1.014) = 45.4°
The angle of incidence, i is gotten from n = sin i/sin r
sin i = nsin r = 1.4sin45.4° = 1.4 × 0.7120 = 0.9968
i = sin⁻¹(0.9968) = 85.44°
Since the girl's eyes are 1.2 m from the ground, the distance ,h from the edge of the cistern she must stand is gotten from
tan i = h/1.2
h = 1.2tan i = 1.2tan85.44° = 1.2 × 12.54 = 15.05 m
h = 15.05 m ≅ 15.1 m
So, she must stand 15.1 m away from the edge of the cistern to still see the object.
