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Q.

The aperture diameter of a plano convex lens is 6 cm and it’s thickness in the middle is 3 mm. If refractive index of the material of the lens is 1.5, find its focal length (in cm).
(Round off to the nearest integer)

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answer is 30.

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Detailed Solution

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From $Δ C A B$

$R^{2} = {(R - 0.3)}^{2} + 3^{2}$

$R^{2} = R^{2} + 0.09 - 0.6 R + 9$

$0.6 R = 9.09$

$R = \frac{90.9}{6} = 15.15 c m$

$\frac{1}{f} = (μ - 1) \frac{1}{R} \Rightarrow f = \frac{R}{μ - 1} = \frac{15.15}{\frac{1}{2}} = 30.3 c m$

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The aperture diameter of a plano convex lens is 6 cm and it’s thickness in the middle is 3 mm. If refractive index of the material of the lens is 1.5, find its focal length (in cm).(Round off to the nearest integer)