To determine the magnification factor of an object placed in front of a convex lens, we can use the lens formula and the magnification formula. Let's break down the problem step-by-step. ### Given Data: - Object distance (u) = -10 cm (the negative sign indicates that the object is placed on the same side as the incoming light) - Image distance (v) = +25 cm (the positive sign indicates that the image is formed on the opposite side of the lens) ### Step 1: Use the Lens Formula The lens formula relates the object distance (u), image distance (v), and the focal length (f) of the lens: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Substituting the values: \[ \frac{1}{f} = \frac{1}{25} - \frac{1}{-10} \] \[ \frac{1}{f} = \frac{1}{25} + \frac{1}{10} \] To add these fractions, we need a common denominator. The least common multiple of 25 and 10 is 50: \[ \frac{1}{25} = \frac{2}{50}, \quad \frac{1}{10} = \frac{5}{50} \] So, \[ \frac{1}{f} = \frac{2}{50} + \frac{5}{50} = \frac{7}{50} \] Thus, \[ f = \frac{50}{7} \approx 7.14 \text{ cm} \] ### Step 2: Calculate the Magnification The magnification (M) produced by a lens is given by the formula: \[ M = \frac{v}{u} \] Substituting the values we have: \[ M = \frac{25}{-10} = -2.5 \] ### Step 3: Interpret the Magnification The negative sign indicates that the image is inverted. The absolute value of the magnification gives us the factor by which the size of the object is increased: \[ |M| = 2.5 \] ### Conclusion The size of the object is increased by a factor of 2.5 when the image is formed on the screen. ### Explanation of Other Options: - **Option A (15.0)**: This value is too high and does not correspond to the calculated magnification. It suggests an unrealistic enlargement of the object size. - **Option C (1.5)**: This value is lower than the calculated magnification. It implies a smaller increase in size than what we found. - **Option D (0.4)**: This value suggests a reduction in size, which contradicts the fact that the image is larger than the object. ### Revision Summary: - The magnification of a lens is calculated using the formula \( M = \frac{v}{u} \). - The object distance (u) is taken as negative for real objects, while the image distance (v) is positive for real images. - The absolute value of magnification indicates how many times larger the image is compared to the object. - In this case, the magnification factor is 2.5, meaning the image is 2.5 times larger than the object.