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,
Mmin = `"D"/"f"=0.25/0.5` = 0.5
and Mmax = `1+"D"/"f"` = 1 + 0.5 = 1.5
Given that, n = 1.5, |R1| = 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`
∴ R2 = `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.
