To determine the apparent displacement of the coin when viewed through a rectangular glass block, we need to apply the principles of refraction and the concept of apparent depth. Let's break this down step-by-step. ### Step 1: Understanding Refraction When light passes from one medium to another (in this case, from air to glass), it changes speed and direction. This bending of light is described by Snell's Law, but for our purposes, we can use a simpler concept known as apparent depth. ### Step 2: Apparent Depth Formula The apparent depth (\(d_a\)) can be calculated using the formula: \[ d_a = \frac{d}{n} \] Where: - \(d\) is the actual depth of the object (the thickness of the glass block in this case). - \(n\) is the refractive index of the medium (the glass block). ### Step 3: Given Values From the problem: - The thickness of the glass block (\(d\)) = 9 cm - The refractive index of the glass (\(n\)) = 1.5 ### Step 4: Calculate Apparent Depth Now, we can substitute the values into the formula: \[ d_a = \frac{9 \text{ cm}}{1.5} \] Calculating this gives: \[ d_a = 6 \text{ cm} \] ### Step 5: Conclusion The apparent displacement of the coin, when viewed from above the glass block, is 6 cm. Therefore, the correct option is **C. 6 cm**. ### Step 6: Analyzing Other Options Now, let's analyze the other options to understand why they are incorrect: - **Option A: 3 cm** - This value is too low. It suggests a misunderstanding of how the refractive index affects the apparent depth. A refractive index of 1.5 means that light travels slower in glass than in air, leading to a greater apparent depth than the actual depth. - **Option B: 5 cm** - This option is also incorrect. It does not align with the calculated apparent depth using the refractive index. It seems to be a miscalculation or misinterpretation of the refractive effect. - **Option D: 8 cm** - This option is too high. It suggests that the light is bending less than it actually does, which would not be the case with a refractive index of 1.5. ### Common Pitfalls - **Misunderstanding the Refractive Index**: Students often confuse the refractive index with the actual depth. Remember, a higher refractive index means that light slows down more, leading to a greater apparent depth. - **Forgetting to Use the Formula**: Always remember to apply the formula for apparent depth when dealing with problems involving refraction through different media. ### Revision Summary - The apparent depth can be calculated using \(d_a = \frac{d}{n}\). - For a glass block of thickness 9 cm and refractive index 1.5, the apparent depth is 6 cm. - The correct answer is **C. 6 cm**. - Always consider how the refractive index affects the perception of depth when light passes through different media.