Maximum Possible Focal Length of a Convex Lens
An image of a small electric bulb fixed on one wall is to be obtained on the opposite wall which is 3 m away using a large convex lens. We determine the maximum possible focal length of the lens required.
Step 1: Given Condition
For real image formation:
Step 2: Condition for Maximum Focal Length
For a fixed object–image separation, focal length is maximum when:
Step 3: Apply Lens Formula
Final Answer
Thus, the maximum focal length of the convex lens that can form a real image on a wall 3 m away is 75 cm. This occurs when the lens is placed midway between the object and the image.
Frequently Asked Questions
Why is the focal length maximum when the lens is placed midway?
For a fixed object–image separation, the focal length becomes maximum when object distance equals image distance (u = v). This occurs when the lens is placed exactly at the midpoint between object and image.
What formula is used to determine the focal length?
The lens formula is used: 1/f = 1/u + 1/v. By applying the condition u = v = D/2, the maximum focal length is obtained.
Can a lens with focal length greater than 0.75 m form the image?
No. If the focal length exceeds 0.75 m, a real image cannot be formed at a fixed object–image separation of 3 m.
Is the image formed real or virtual in this setup?
The image formed on the opposite wall is real, since it can be projected onto a surface.
What is the maximum focal length calculated in this problem?
The maximum possible focal length of the convex lens is 0.75 m (75 cm).