A bi-convex lens has radius of curvature of both the surfaces same as 
. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides ( 
), without any change in lens power then possible combination of 
and 
is:
and 
and 
and 
and 
Text Solution
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To replace a bi-convex lens with another convex lens that has different radii of curvature on each side (i.e., 
), while maintaining the same lens power, the radii must satisfy a specific relationship.
For the current bi-convex lens, both radii of curvature are given as 
. The lens formula for power is tied to the radii through:
When this lens is replaced by a lens with different radii ( 
and 
), the condition that has to be met is:
For power equivalence, the expressions for 
and 
must be equal:
This simplifies to:
Given 
, it follows that:
Thus, simplifying the equation gives:
Therefore, any valid pair of radii 
and 
must satisfy this equation.
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