Question

Солнце составляет с горизонтом угол, синус которого равен 0.6. Шест высотой 170 см вбит в дно водоёма глубиной 80 см. Найдите длину тени на дне водоёма, если показатель преломления воды 4/3.

Answer 1

Ответ:

sin(c) = 0.6, откуда cos(c)=(1^2-0.6^2)^0.5 = 0.8, значит tan(c) = sin(c)/cos(c) = 3/4

из воды торчит 170-80=90 см = 0.9 м

Значит длина тени на поверхности воды составит s1 = 0.9 м / tan(c) = 1.2 метра

Затем будет преломление по закону Снеллиуса:

sin(a)*1 = sin(b)*4/3

cos(b)*1 = sin(b)*4/3

sin(b) = 0.8/(4/3) = 0.6, откуда b=с

значит s2 = 0.8м*tan(b) = 0.8*3/4 = 0.6 метра

Полная длина тени по дну составит s1+s2 = 1.8 м

Answer 2

Calculation of the Length of the Shadow

To find the length of the shadow on the bottom of the pond, we can use the concept of similar triangles. Let's denote the length of the shadow as x.

Given: - The height of the pole (h) = 170 cm - The depth of the pond (d) = 80 cm - The angle between the sun and the horizon (θ) = arcsin(0.6) - The refractive index of water (n) = 4/3

Using the concept of similar triangles, we can set up the following proportion:

h / x = (h + d) / (x + d)

Simplifying the equation, we get:

h(x + d) = x(h + d)

Expanding the equation, we have:

hx + hd = xh + xd

Rearranging the terms, we get:

hx - xh = xd - hd

Factoring out the common terms, we have:

x(h - h) = d(x - h)

Since (h - h) and (x - h) are both equal to zero, the equation simplifies to:

0 = 0

This means that the length of the shadow on the bottom of the pond is undefined or zero. This is because the angle of incidence is equal to the critical angle, resulting in total internal reflection. As a result, no light is transmitted into the water, and the shadow is not formed.

Therefore, the length of the shadow on the bottom of the pond is undefined or zero.

Please let me know if you need any further clarification.