Question

A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index of the first lens is \(1.5\) and that of second is \(1.2\). Both the curved surfaces are of the same radius of curvature \(R=14\) cm. For an object distance of \(40\) cm, the image distance will be

• A. \(280.0\) cm
• B. \(13.3\) cm
• C. \(21.5\) cm
• D. \(40.0\) cm

Hint:

The two halves are plano-convex lenses in contact, so their powers add. Then use the lens formula for the given object distance.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The biconvex lens is made of two thin plano-convex lenses placed in contact.
For thin lenses in contact the powers add: \(\dfrac{1}{f}=\dfrac{1}{f_1}+\dfrac{1}{f_2}\).

Step 2: Focal Lengths
For a plano-convex lens, \(\dfrac{1}{f}=(n-1)\dfrac{1}{R}\).
\(\dfrac{1}{f_1}=\dfrac{0.5}{14}\) and \(\dfrac{1}{f_2}=\dfrac{0.2}{14}\)

Step 3: Combined Focal Length
\(\dfrac{1}{f}=\dfrac{0.7}{14}=\dfrac{1}{20}\), so \(f=20\) cm.

Step 4: Calculation
Using \(\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}\) with \(u=-40\) cm:
\(\dfrac{1}{v}=\dfrac{1}{20}-\dfrac{1}{40}=\dfrac{1}{40}\)
So \(v=40\) cm, which is option (D).

Final Answer:
The image forms at a distance of 40 cm from the lens. \[ \boxed{\text{(D) }\text{40.0 cm}} \]