Exemplar Problems

Problem 3 : Lens Combination

Problem Statement: Two lenses of focal lengths f₁ and f₂ are placed in contact. Calculate the effective focal length of the combination.

Solution :

• Use the lens formula for each lens: $$\frac{1}{f_1} = \frac{1}{v_1} - \frac{1}{u_1}$$ and $$\frac{1}{f_2} = \frac{1}{v_2} - \frac{1}{u_2}$$, where f₁ and f₂ are the focal lengths, and u₁ and u₂ are the object distances.
• Step 2: Since the lenses are in contact, the image formed by the first lens becomes the object for the second lens. So, v₁ for the first lens becomes u₂ for the second lens.
• Step 3: Calculate v₁ using the lens formula for the first lens and u₂ using the lens formula for the second lens.
• Step 4: The effective focal length $F$ of the combination is given by $$(F = \frac{f_1 f_2}{f_1 + f_2}).$$