The refractive index of water is 1.33. The direction in which a man under water should look to see the setting sun is

Options

A. 49 to the horizantal
B. 90 with the vertical
C. 49 to the vertical
D. Along the horizontal

Answer

To solve the problem of determining the direction in which a man underwater should look to see the setting sun, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Situation**: The man is underwater and wants to see the setting sun. The sun is above the water surface, and the light rays from the sun will enter the water and refract.

2. **Identify the Refractive Index**: The refractive index of water (μ) is given as 1.33. This means that light travels slower in water than in air.

3. **Apply Snell's Law**: Snell's Law relates the angles of incidence and refraction when light passes from one medium to another. It is given by:
\[ \mu_1 \sin(i) = \mu_2 \sin(r) \]
where:
- \( \mu_1 \) is the refractive index of air (approximately 1),
- \( \mu_2 \) is the refractive index of water (1.33),
- \( i \) is the angle of incidence (the angle at which light hits the water surface),
- \( r \) is the angle of refraction (the angle at which light travels in water).

4. **Determine the Angle of Incidence**: Since the sun is setting, we can assume that the rays of sunlight are coming in at an angle of 90 degrees to the water surface (i.e., they are horizontal).

5. **Substitute Values into Snell's Law**:
\[ 1 \cdot \sin(90^\circ) = 1.33 \cdot \sin(r) \]
Since \( \sin(90^\circ) = 1 \), we have:
\[ 1 = 1.33 \cdot \sin(r) \]

6. **Solve for \( \sin(r) \)**:
\[ \sin(r) = \frac{1}{1.33} \approx 0.75187 \]

7. **Calculate the Angle of Refraction \( r \)**: To find the angle \( r \), we take the inverse sine:
\[ r = \sin^{-1}(0.75187) \]
Using a calculator or sine table, we find:
\[ r \approx 49^\circ \]

8. **Interpret the Result**: The angle \( r \) is measured from the normal (which is vertical). Therefore, the man should look at an angle of \( 49^\circ \) from the vertical to see the setting sun.

### Final Answer:
The man underwater should look at an angle of **49 degrees from the vertical** to see the setting sun.

---