A symmetrical biconvex lens of focal length 'f' is cut into four identical pieces along and perpendicular to its principal axis The focal length of each of four pieces is

CONCEPT:

• Lens: The transparent curved surface which is used to refract the light and make an image of any object placed in front of it is called a lens.
  • Convex lens: ​A lens having two spherical surfaces, bulging outwards is called a double convex lens (or simply convex lens).
    • It is thicker in the middle as compared to the edges.
  • Convex lenses converge light rays and hence, convex lenses are also called converging lenses.

EXPLANATION:

• The lens maker’s formula is given by:

\(⇒ \frac{1}{f} = \left( {n - 1} \right)\left( {\frac{1}{{{R_1}}} - \frac{1}{{{R_2}}}} \right)\)

Where, f is the focal length (half the radius of curvature), n is the refractive index of the material used, R1 is the radius of curvature of sphere 1 and R2 is the radius of curvature of sphere 2

• For equiconvex lens

\(⇒ \frac{1}{f} = \left( {n - 1} \right)\left( {\frac{1}{{{R}}} + \frac{1}{{{R}}}} \right)=(n-1)\frac{2}{R}\)      -------- (1)

• If a biconvex lens is cut perpendicular to its principal axis, then it will become the plano-convex lens and then the focal length of the plano-convex lens is 

\(⇒ \frac{1}{f'} =(n-1)\frac{1}{R}\)      ------ (2)

From 1 and 2, we get

⇒ f' = 2f

• The focal length of each of the four pieces is 2f. Therefore option 3 is correct.