A convex lens has a focal length f. It is cut inti two parts along the dotted lines as shown ii figure. The focal length of each part will be …....... .

Options

A. `f/2`
B. f
C. 3f
D. 2f

Answer

B, D

Explanation

For convex lens,
`1/f=(n-1)(1/R_1-1/R_2)(R_1=R,R_2=-R)`
`=(n-1)(1/R+1/R)=(n-1)(2/R)`
`thereforef=(R)/(2(n-1))` …......(1)
Now a convex lens is cut into two parts along perpendicular direction to the axis, the plano convex lens will prepared. The focallength of this lens is `f_1` then,
`(1)/(f_1)=(n-1)(1/R_1-1/R_2)`
`[R_1=prop(infinite),R_2=-R]`
`therefore1/f_1=(n-1)1/R`
`therefore f_1=(R)/(n-1)=2f`