Question

An underwater scuba diver sees the Sun at an apparent angle of 47.5° above the horizontal. What is the actual elevation angle of the Sun above the horizontal? (Use 1.333 for the index of refraction of water.)

Answer 1

actual elevation angle above horizontal =
`90{\circ} - 64.232{\circ} = 25.768^(\circ)`

Given:

apparent angle =
`47.5^(\circ)`

refractive index of water,
`\mu _(w)` = 1.333

Solution:

angle of incidence,
`\angle i = 90{\circ} - 47.5{\circ} = 42.5^(\circ)`

refractive index of water,
`\mu _(a)` = 1

Using Snell's law:

`\mu _(a)sini = \mu _(w)sinr`

`sinr =  \mu _(w)sini = 1.333sin42.5^(\circ)`

`r =sin^(-1)0.90056 = 64.232^(\circ)`

angle of refraction,
`\angle r = 64.232^(\circ)`

Now,

actual elevation angle above horizontal =
`90{\circ} - 64.232{\circ} = 25.768^(\circ)`