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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?

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1. Given Data

  • Distance between Object and Image (L): 3 m
  • Type of Lens: Convex Lens

2. Concept

For a convex lens to form a real image of an object on a screen, the distance between the object and the screen (L) must be at least 4 times the focal length (f).

Mathematically:

L ≥ 4f

Therefore, for a fixed distance L, the maximum focal length possible is when L = 4f.

3. Calculation

We rearrange the formula to find the maximum focal length (fmax):

fmax = L / 4

Substituting the value of L = 3 m:

fmax = 3 / 4

fmax = 0.75 m

Maximum Focal Length = 0.75 m

Conclusion: The maximum focal length of the lens required is 0.75 m (or 75 cm). If the focal length is greater than this, no sharp image will be formed on the wall.

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