Lenses are constructed by a material of refractive index $1.50$ . The magnitude of the radii of curvature are $20 c m$ and $30 c m$ . Find the focal lengths of the possible lenses with the above specifications.

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Solution

Given $μ = 1.5$
Magnitude of radii of cirvatures $= 20 c m$ and $30 c m$
The 4 types of possible lens are as below.
$\frac{1}{f} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

Case (1) : (Double convex ) $[R_{1} = + v e, R_{2} = - v e]$

$\frac{1}{f} = (15 - 1) (\frac{1}{20} - \frac{1}{30})$

$\Rightarrow f = 24 c m$

Case (2) : (Double concave) $[R_{1} = - v e, R_{2} = + v e]$

$\frac{1}{f} = (15 - 1) (\frac{- 1}{20} - \frac{1}{30})$

$\Rightarrow f = - 24 c m$

Case (3) : (Concave concave) $[R_{1} = - v e,, R_{2} = - v e]$

$\frac{1}{f} = (15 - 1) (\frac{1}{- 20} - \frac{1}{30})$

$\Rightarrow f = - 120 c m$

Case (4) : (Concave convex) $[R_{1} = + v e, R_{2} = + v e]$

$\frac{1}{f} = (15 - 1) (\frac{1}{20} - \frac{1}{30})$

$\Rightarrow f = + 120 c m$

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Lenses are constructed by a material of refractive index 1.50. The magnitude of the radii of curvature are 20cm and 30cm. Find the focal lengths of the possible lenses with the above specifications.

Lenses are constructed by a material of refractive index $1.50$ . The magnitude of the radii of curvature are $20 c m$ and $30 c m$ . Find the focal lengths of the possible lenses with the above specifications.