Answer:
a The diagram of the situation is shown on the first uploaded image
b the angle of incidence beam striking the water is ![\theta = 49.63^o](https://tex.z-dn.net/?f=%5Ctheta%20%3D%2049.63%5Eo)
c the angle of refraction beam striking the water is ![r = 59.7^o](https://tex.z-dn.net/?f=r%20%3D%2059.7%5Eo)
d The angle the refracted beam make with respect to the horizontal is ![= 30.3^o](https://tex.z-dn.net/?f=%3D%2030.3%5Eo)
e The height of the target above sea level is
![h= 125.05m](https://tex.z-dn.net/?f=h%3D%20125.05m)
Explanation:
From the diagram we see that the angle of the beam striking the water is
![tan \theta = \frac{100}{85}](https://tex.z-dn.net/?f=tan%20%5Ctheta%20%3D%20%5Cfrac%7B100%7D%7B85%7D)
![\theta = tan^{-1}(\frac{100}{85} )](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%5E%7B-1%7D%28%5Cfrac%7B100%7D%7B85%7D%20%29)
![= 49.63^o](https://tex.z-dn.net/?f=%3D%2049.63%5Eo)
According to Snell's law
![\mu_{water} *sin(i) = \mu_{air} *sin(r)](https://tex.z-dn.net/?f=%5Cmu_%7Bwater%7D%20%2Asin%28i%29%20%3D%20%5Cmu_%7Bair%7D%20%20%2Asin%28r%29)
Where
is the refractive index of water = 1.333
is the angle of incidence
is the refractive index of air = 1
r is the angle of refraction
Substituting values accordingly
![1.33 * sin (40.37) = 1 * sin(r)](https://tex.z-dn.net/?f=1.33%20%2A%20sin%20%2840.37%29%20%3D%201%20%2A%20sin%28r%29)
Making r the subject of the formula
![r = sin^{-1}(\frac{1.333 *sin(40.37)}{1})](https://tex.z-dn.net/?f=r%20%3D%20sin%5E%7B-1%7D%28%5Cfrac%7B1.333%20%2Asin%2840.37%29%7D%7B1%7D%29)
![= 59.7^o](https://tex.z-dn.net/?f=%3D%2059.7%5Eo)
looking at the diagram we can see that to obtain the angle the refraction beam makes with the horizontal by subtracting the angle refraction from 90°
i.e
°
From the diagram we see that the height target above sea level can be obtained by this relation
![tan \theta = \frac{h}{214}\\](https://tex.z-dn.net/?f=tan%20%5Ctheta%20%3D%20%5Cfrac%7Bh%7D%7B214%7D%5C%5C)
Where h is the is the height
![tan(30.3) = \frac{h}{214}](https://tex.z-dn.net/?f=tan%2830.3%29%20%3D%20%5Cfrac%7Bh%7D%7B214%7D)
![h = 214 * tan (30.3)](https://tex.z-dn.net/?f=h%20%3D%20214%20%2A%20tan%20%2830.3%29)
![=125.05m](https://tex.z-dn.net/?f=%3D125.05m)