A ray of sunlight hits a frozen lake at a 45° angle of incidence. At what angle of refraction does the ray penetrate the ice? At what angle does it penetrate the water beneath the ice?

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A ray of sunlight hits a frozen lake at a 45° angle of incidence. At what angle of refraction does the ray penetrate the ice? At what angle does it penetrate the water beneath the ice?

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Answer 1 · 2016-12-19T23:48:01

Angle of refraction at the air-ice interface $=32.7^@$
Angle of refraction at the ice-water interface $=32.1^@$

Explanation:

Using the following refractive indices
Air $=1.00$
Water $=1.33$
Ice $=1.31$

Using Snell's Law of refraction applicable for a ray crossing the interface between two media which have refractive indices $n_1$ and $n_2$ as shown in the figure.

wikipedia

$n_1 sinθ_1 = n_2 sinθ_2$
where $θ_1 and θ_2$ are the angles of incidence and refraction respectively.

For first interface when ray enters from air to ice
$1.00xxsin 45 = 1.31xxsin theta_2$
$=>sin theta_2 =(sin 45/1.31)= 0.5398$ , rounded to four decimal places
$=>theta_2 =sin^-1(0.5398)=32.7^@$ , rounded to one decimal place.

Due to geometry this becomes angle of incidence for the second interface as ray enters from ice to water. Using Snell's law again we have

$1.31xxsin 32.67 = 1.33 xxsin theta_2$
$theta_2 = sin^-1((1.31xx0.5398)/1.33)=32.1^@$ , rounded to one decimal place

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A ray of sunlight hits a frozen lake at a 45° angle of incidence. At what angle of refraction does the ray penetrate the ice? At what angle does it penetrate the water beneath the ice?

1 Answer

Explanation:

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