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An object and a screen are 75 cm apart. Where should a convex lens of focal length 12 cm be placed between them so that a real image of the object is formed on the screen?

1. 15 cm from the object
2. 45 cm from the image
3. 60 cm from the object
4. 30 cm from the image

Correct answer: 15 cm from the object

Solution

Using the lens formula with object at distance u from lens (u > 0) and image at v = 75 - u: 1/(75 - u) + 1/u = 1/12 => 75*u = 900 + 75u - u²... simplifying: u² - 75u + 900 = 0 => u = (75 +/- 45)/2 => u = 60 cm or u = 15 cm. Both give real images. The options 15 cm from object and 60 cm from object are both correct positions. The answer listed here is 15 cm from the object (the other valid position, 60 cm from object, is option C).

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