To solve the problem of finding the position of the slide from the lens in a projection lantern setup, we can use the lens formula and the magnification formula. Let's break down the steps clearly. ### Step 1: Understand the Problem We are given: - The magnification (M) of the image is 24 (the image is 24 times larger than the slide). - The distance from the lens to the screen (image distance, v) is 72.0 m. We need to find the object distance (u), which is the distance from the lens to the slide. ### Step 2: Use the Magnification Formula The magnification (M) in a lens system is given by the formula: \[ M = -\frac{v}{u} \] Where: - \( M \) is the magnification, - \( v \) is the image distance (distance from the lens to the screen), - \( u \) is the object distance (distance from the lens to the slide). Since the image is upright and enlarged, we can take the magnification as positive: \[ M = \frac{v}{u} \] Substituting the known values: \[ 24 = \frac{72.0}{u} \] ### Step 3: Solve for Object Distance (u) Rearranging the equation to solve for \( u \): \[ u = \frac{72.0}{24} \] Calculating this gives: \[ u = 3.0 \, \text{m} \] ### Step 4: Conclusion The position of the slide from the lens is **3.0 m**. Therefore, the correct option is **B**. ### Step 5: Explanation of Other Options - **Option A (0.3 m)**: This would imply a much larger magnification than 24, which is not possible given the image distance of 72.0 m. - **Option C (3.5 m)**: This would result in a magnification less than 24, which contradicts the problem statement. - **Option D (4.0 m)**: Similar to option C, this would also yield a magnification less than 24, which is incorrect. ### Summary of Key Points - The magnification formula relates the image distance and object distance. - The object distance can be calculated by rearranging the magnification formula. - The correct answer is found to be 3.0 m, which corresponds to option B. - Understanding the relationship between object distance, image distance, and magnification is crucial in lens problems. This thorough breakdown should help you understand how to approach similar problems in the future!