To determine the apparent distance of the stone from the boy looking from the surface of the river, we need to apply the concept of refraction and the formula that relates the real depth of an object to its apparent depth when viewed through a medium with a different refractive index. ### Step-by-Step Explanation 1. **Understanding Refraction**: When light travels from one medium to another (in this case, from water to air), it changes speed, which causes it to bend. This bending of light makes objects appear at different positions than they actually are. The refractive index (n) quantifies how much the light bends when it enters a new medium. 2. **Given Data**: - Real depth of the stone (d) = 6.0 m - Refractive index of water (n) = 4/3 3. **Formula for Apparent Depth**: The relationship between the real depth (d) and the apparent depth (d') can be expressed using the formula: \[ d' = \frac{d}{n} \] where: - \(d'\) = apparent depth - \(d\) = real depth - \(n\) = refractive index of the medium (water in this case) 4. **Calculating Apparent Depth**: - Substitute the values into the formula: \[ d' = \frac{6.0 \, \text{m}}{4/3} \] - To divide by a fraction, we multiply by its reciprocal: \[ d' = 6.0 \, \text{m} \times \frac{3}{4} = \frac{18.0}{4} = 4.5 \, \text{m} \] 5. **Conclusion**: The apparent distance of the stone from the boy is 4.5 m. Therefore, the correct option is **D. 4.5m**. ### Explanation of Other Options - **Option A (8.0m)**: This option is incorrect because it suggests that the stone appears further away than it actually is. The refractive index indicates that the stone will appear closer due to the bending of light. - **Option B (5.5m)**: This option is also incorrect. It does not take into account the correct application of the refractive index. The apparent depth must be less than the real depth when viewed from above the water. - **Option C (5.0m)**: This option is incorrect for similar reasons as above. It underestimates the effect of the refractive index, which causes the stone to appear closer than its actual depth. ### Common Pitfalls - **Ignoring the Refractive Index**: A common mistake is to assume that the apparent depth is the same as the real depth without considering the refractive index. - **Misapplying the Formula**: Ensure that you are using the correct formula for apparent depth and that you understand how to manipulate fractions correctly. ### Revision Summary - The apparent depth of an object in a medium is calculated using the formula \(d' = \frac{d}{n}\). - The refractive index of water (4/3) indicates that objects appear closer than they are when viewed from above. - The correct apparent distance of the stone is 4.5 m, making option D the right choice. - Always remember to apply the refractive index correctly to avoid errors in calculations.