Question

In the figure below, point A is the object and point B is the image formed by the lens. Let \( l_1, l_2 \) and \( l_3 \) denote the optical path lengths of the three rays 1, 2 and 3, respectively. Identify the correct statement. 

• A. \( l_1 = l_2 = l_3 \)
• B. \( l_1>l_2<l_3 \)
• C. \( l_1 = l_3<l_2 \)
• D. \( l_1 = l_3>l_2 \)

Hint:

In image formation by a lens or mirror, the optical path lengths for all rays from the same object point to the same image point are equal, ensuring constructive interference.

Answer 1

The Correct Option is A

Step 1: Understanding the principle.
When a lens forms a sharp image, all rays originating from the same point on the object and converging to a single image point must have equal optical path lengths between the object and image points. This ensures constructive interference at the image point.
Step 2: Analyzing the rays.
In the figure, rays 1, 2, and 3 travel through different parts of the lens, but the optical path length \( n \times l \) (where \( n \) is the refractive index and \( l \) is the physical length) for all three rays is the same. This is because the lens introduces phase compensation so that all rays arrive in phase at point B.
Step 3: Conclusion.
Hence, \( l_1 = l_2 = l_3 \).