A symmetric double convex lens is cut in two equal parts by a plane perpendicular to the principle axis. If the power of the original lens is 4D, the power of a cut lens will be
3D
4D
5D
2D
A
3D
B
5D
C
4D
D
2D
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Solution
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As the convex lens is symmetric on both sides, i.e R1=R2=R
When the lens in not cut:
Using lens maker formula:
1f=(μ−1)(1R1−1R2)
1f=(μ−1)(1R−1−R)=2R(μ−1)
Power of lens, P=1f
⇒4D=2R(μ−1)
⇒μ−1R=2D .........(1)
Now the lens in cut perpendicular to the principal axis:
R1=R and R2=∞
Using lens maker formula:
1f=(μ−1)(1R1−1R2)
1f′=(μ−1)(1R−1∞)=1R(μ−1)
Power of lens, P′=1f′==1R(μ−1)=2D .......... using (1)
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