Question

a biconvex lens has a focal length 2/3 times the radius of curvature of other faces. calculate the refractive index of lens material

Answer 1

Final Answer : 7/4

Assuming surrounding medium is air or vacuum.
Steps:
1) Radius of Curvature , R(1) = R (say)
Radius of Curvature, R(2) = -R
n - > refractive index of lens.
f = 2R/3 (given)

2) By Lens Makers Formula,
$\frac{1}{f} = ( \frac{n}{1} - 1)( \frac{1}{r(1)} - \frac{1}{r(2)} ) \\ = > \frac{1}{ \frac{2r}{3} } = ( n - 1)( \frac{1}{r} - \frac{1}{( - r)} ) \\ = > \frac{3}{2r} = (n -1 ) \frac{2}{r} \\ = > n - 1 = \frac{3}{4} \\ = > n = \frac{7}{4}$

Hence, Refractive Index of Lens is 7/4.