Question

Calculate the radius of curvature of an equi-concave lens of refractive index 1.5, when it is kept in a medium of refractive index 1.4, to have a power of -5D? 

Answer 1

Using lens maker formulae for given equal concave lens,

`1/f = (n_2/n_1 - 1)(1/-R - 1/R)`

⇒ `1/f = (n_2/n_1 - 1)(-2/R)`

Where n₂ and n₁ are refractive index of the lens and medium, respectively where  

n₂ = 1.5 & n₁ = 1.4

Power of lens -5D

Focal length `f = 1/-5 xx 100 = -20`cm

Putting all the values in equation 1,

⇒ `1/-20 = (1.5/1.4 - 1)(-2/R)`

⇒ `1/20 = (0.1/1.4)(2/R)`

⇒ R = `4/1.4 = 2.86` cm