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 $$(F = \frac{f_1 f_2}{f_1 + f_2}).$$
BETA
