The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall 3m away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose?
The maximum possible focal length of the lens is 75 cm.
Explanation
This question tests the understanding of lens formula and the condition for forming real images. For a convex lens to form a real image on a screen, both object and image must be on opposite sides of the lens. The key insight is that the minimum distance between a real object and its real image formed by a convex lens is 4f (achieved when object is at 2f and image is at 2f). Since the walls are fixed at 3m apart, this distance must be at least 4f. Therefore, 4f 3m, giving f 0.75m or 75cm. This is the maximum focal length possible.
Solution Steps
Step 1: Given: Distance between object (bulb on wall) and image (opposite wall) = D = 3m.
Step 2: For a convex lens to form a real image, the minimum distance between object and image is 4f, which occurs when object is placed at 2f from the lens (image then forms at 2f on the other side).
Step 3: Therefore, for the image to be obtained on the opposite wall: 4f D or 4f 3m.
Step 4: Solving: f 3/4 m = 0.75 m = 75 cm.
Step 5: Hence, the maximum possible focal length = 75 cm.