An asymmetrical biconvex lens made of glass (refractive index 1.5 ) has the ratio of its radii of curvature as 1:2 . When this lens is completely immersed in water (refractive index 4 3 ), its focal length is found to be 64 cm . The radius of curvature of the steeper surface of the lens is:

Step-by-step solution

Let the radii of curvature of the biconvex lens be R and 2R . The steeper surface corresponds to the smaller radius of curvature, which is R . According to the sign convention for a biconvex lens, R₁ = +R and R₂ = -2R . The Lens Maker's formula for a lens immersed in a medium is given by: 1 f_m = ( _L _m - 1 ) ( 1 R₁ - 1 R₂ ) Substitute the given values into the formula: 1 64 = ( 1.5 4/3 - 1 ) ( 1 R - 1 -2R ) Simplify the relative refractive index term: 1.5 4/3 = 3/2 4/3 = 9 8 Now, substitute this back into the equ