Question

Во сколько раз длина тени от вертикального шеста в воздухе больше длины тени того же шеста в воде при его полном погружении? Углы падения лучей в обоих случаях одинаковы.

Answer 1

h1/h2=(H*tga)/(H*tgb).

Отношение теней относится как тангесы углов падения в воздухе и воде.

Учитывая формулы: tg^2a=1+1/sqrt(1-sin^2a) и sina=n*sinb (n - показатель преломления в воде), находим ответ.

Answer 2

Calculating the Length of Shadow in Air and Water

When calculating the length of the shadow cast by a vertical pole in air and water, the key factor to consider is the refractive index of water, which affects the path of light rays passing through it.

In air: The length of the shadow cast by a vertical pole in air can be calculated using basic trigonometry. If the height of the pole is *h* and the length of the shadow is *s*, then the ratio of the length of the shadow to the height of the pole is given by the tangent of the angle of elevation of the sun.

In water: When the same pole is fully submerged in water, the light rays passing through the water are refracted due to the change in medium. The refractive index of water causes the light rays to bend, affecting the length of the shadow.

Ratio of Shadow Lengths in Air and Water

The ratio of the length of the shadow in air to the length of the shadow in water when the angles of incidence are the same can be calculated using the principles of refraction.

The refractive index of water is approximately 1.33. This means that light travels 1.33 times faster in air than in water. As a result, the length of the shadow in water will be longer compared to the length of the shadow in air.

Using the refractive index of water, the ratio of the length of the shadow in air to the length of the shadow in water can be calculated as follows:

Ratio = (Refractive index of air) / (Refractive index of water) = 1 / 1.33 ≈ 0.75.

Therefore, the length of the shadow in water is approximately 0.75 times the length of the shadow in air when the angles of incidence are the same.

This ratio accounts for the difference in the speed of light in air and water, leading to the longer shadow in water compared to air when the same pole is fully submerged.

I hope this explanation helps! If you have further questions or need additional information, feel free to ask.