**Solve Numerical example.**

A person uses spectacles of ‘number’ 2.00 for reading. Determine the range of magnifying power (angular magnification) possible. It is a concavoconvex lens (n = 10.5) having a curvature of one of its surfaces to be 10 cm. Estimate that of the other.

#### Solution

For a single concavo-convex lens, the magnifying power will be the same as that for a simple microscope As the number represents the power of the lens,

P = `1/"f"` = 2 ⇒ f = 0.5 m.

∴ Range of magnifying power of a lens will be,

M_{min} = `"D"/"f"=0.25/0.5` = 0.5

and M_{max} = `1+"D"/"f"` = 1 + 0.5 = 1.5

Given that, n = 1.5, |R_{1}| = 10 cm

f = 0.5 m = 50 cm

From lens maker’s equation,

`1/"f"=("n"-1)(1/"R"_1-1/"R"_2)`

`1/50=(1.5-1)(1/10-1/"R"_2)`

∴ 0.04 = `(1/10-1/"R"_2)`

∴ `1/"R"_2=1/10-0.04=3/50`

∴ R_{2 }= `50/3` cm

The range of magnifying power is from **0.5** to **1.5 **radius of curvature of other surface is **`50/3` cm**.