Question

Power of a biconvex lens is \( P \) diopter. When it is cut into two symmetrical halves by a plane containing the principal axis, the ratio of the power of two halves is:

• A. 1:2
• B. 2:1
• C. 1:4
• D. 1:1

Hint:

When a lens is cut along the principal axis, its focal length remains unchanged, and hence its power remains the same.

Answer 1

The Correct Option is D

Step 1: {Understanding the Concept of Lens Power} 
The power of a lens is given by: \[ P = \frac{1}{f} \] where \( f \) is the focal length of the lens. 
Step 2: {Effect of Cutting a Lens Along the Principal Axis} 
When a symmetrical biconvex lens is cut into two halves along the principal axis, the focal length remains the same for each half.
Since power is inversely proportional to focal length, the power of each half remains unchanged.
Thus, the ratio of power between the two halves is: \[ 1:1 \] Thus, the correct answer is \( 1:1 \). 
 

Answer 2

Step 1: Understand the meaning of power of a lens
The power \( P \) of a lens is the reciprocal of its focal length (in meters):
\( P = \frac{100}{f(\text{cm})} \)
Where a positive value indicates a converging (convex) lens.

Step 2: Consider cutting the biconvex lens along a plane containing the principal axis
When a biconvex lens is cut symmetrically along the principal axis (i.e., into two equal halves through its center), each half retains the same curvature on its surfaces.

Step 3: Effect on focal length and power
Each half behaves like a plano-convex lens (one flat surface and one curved surface), but the focal length of each remains the same as the original lens.
Therefore, each half retains the same power as the original lens, because the refracting surfaces remain unchanged in shape and position.

Step 4: Determine the ratio of powers
Since both halves are symmetrical and have identical geometry and optical properties:
Their powers are equal.

Step 5: Final Answer
The ratio of the power of the two halves is:
1:1