Question

Determine the direction in which a fish under water sees the setting sun. Refraction under water is 1.33

• A. Below the horizon
• B. At the horizon
• C. Above the horizon
• D. The sun is not visible

Answer 1

Answer: (C)

Above the horizon

Answer 2

When light travels from air to water, it bends towards the normal due to refraction. The fish, being underwater, sees the sun along the path of the refracted light rays.

Let $n_{air} = 1.00$ be the refractive index of air and $n_{water} = 1.33$ be the refractive index of water. Let $\theta_i$ be the angle of incidence in air and $\theta_r$ be the angle of refraction in water, both measured with respect to the normal to the water surface.

For the setting sun, the light rays are coming from the horizon in the air. This means the angle of incidence with the normal is $\theta_i = 90^\circ$.

Using Snell's Law: $n_{air} \sin \theta_i = n_{water} \sin \theta_r$ $1.00 \times \sin 90^\circ = 1.33 \times \sin \theta_r$ $1 \times 1 = 1.33 \sin \theta_r$ $\sin \theta_r = \frac{1}{1.33}$

Calculating the angle of refraction: $\theta_r = \arcsin\left(\frac{1}{1.33}\right) \approx 48.75^\circ$

This angle $\theta_r$ is measured with respect to the normal. The angle the refracted ray makes with the horizontal water surface is $90^\circ - \theta_r$. Angle with horizontal $= 90^\circ - 48.75^\circ = 41.25^\circ$.

Since this angle is positive, the refracted ray is directed above the horizontal. The fish sees the sun along the direction of this refracted ray. Therefore, the fish sees the setting sun at an angle of approximately $41.25^\circ$ above the horizon.