A Convex lens having a power of one dioptre is made of glass having refractive index 1.48. What will be the power of convex lens made of material with refractive index 1.6 and same dimension

1.25 D

The correct answer is Option (2) → 1.25 D

$P=\frac{1}{f}=(μ-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$ [Lens maker formula]

where,

P = Power of lens

μ = Refractive index

$R_1$ and $R_2$ = Radius of curvature of lens.

Now,

$P_1=\frac{1}{f_1}=(μ_1-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

$P_2=\frac{1}{f_2}=(μ_2-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$ [Dimension same]

$\frac{P_1}{P_2}=\frac{μ_1-1}{μ_2-1}$

$⇒P_2=P_1\frac{μ_2-1}{μ_1-1}$

$P_2=1.\frac{1.6-1}{1.48-1}$

$=1.25D$