AP TET Paper 2 Math and Science Model Paper 2

Concept:A biconvex lens cut perpendicular to its principal axis becomes a plano-convex lens, whose focal length becomes double.Cutting along the principal axis does not change the curvature of the surfaces, so the focal length remains unchanged.Explanation:For a symmetrical biconvex lens with both radii equal to $R$, the lens maker’s formula gives:$$\frac{1}{f} = (n-1)\left(\frac{1}{R} - \frac{1}{-R}\right) = (n-1)\frac{2}{R}$$Now, when the lens is cut perpendicular to the principal axis, each piece has one curved surface of radius $R$ and one flat surface of radius $\infty$.So, the focal length $f'$ of each plano-convex piece is:$$\frac{1}{f'} = (n-1)\left(\frac{1}{R} - \frac{1}{\infty}\right) = (n-1)\frac{1}{R}$$Comparing the two equations, we get:$$\frac{1}{f'} = \frac{1}{2f} \Rightarrow f' = 2f$$The second cut along the principal axis only splits the piece further without affecting its curvature.Therefore, each of the four identical pieces has focal length $2f$.Answer:Option C: $2f$