Question

A symmetric double convex lens is cut into two equal parts by a plane perpendicular to the principal axis. If the power of the original lens is \(4D\), the difference between the powers of the original lens and the cut lens is

• A. zero
• B. \(3D\)
• C. \(D\)
• D. \(2D\)

Hint:

When a symmetric double convex lens is cut perpendicular to the principal axis, each part becomes plano-convex and its power becomes half of the original power.

Answer 1

The Correct Option is D

Step 1: Understand the cutting of lens.
A symmetric double convex lens is cut into two equal parts by a plane perpendicular to the principal axis. This means each part becomes a plano-convex lens.

Step 2: Power of original lens.
The power of original symmetric double convex lens is given as:
\[ P = 4D \]

Step 3: Effect of cutting perpendicular to principal axis.
When a symmetric double convex lens is cut into two equal parts perpendicular to the principal axis, each half has only one curved surface and one plane surface. Therefore, power of each cut lens becomes half of the original power.
\[ P' = \frac{P}{2} \]

Step 4: Substitute the value of original power.
\[ P' = \frac{4D}{2} \]
\[ P' = 2D \]

Step 5: Find the difference in powers.
\[ \text{Difference} = P - P' \]
\[ \text{Difference} = 4D - 2D \]
\[ \text{Difference} = 2D \]

Step 6: Final conclusion.
\[ \boxed{2D} \] Hence, correct answer is option (D).