Question

# Diameter of a plano-convex lens is $$6\ cm$$ and thickness at the centre is $$3\ mm$$. If speed of light in material of lens is $$2\times 10^8\ m/s$$, the focal length of the lens is?

A
15 cm
B
20 cm
C
30 cm
D
10 cm

Solution

## The correct option is C $$30\ cm$$According to lens formula $$\dfrac {1}{f}=(\mu -1)\left[\dfrac {1}{R_1}-\dfrac {1}{R_2}\right]$$The lens plano-convex i.e., $$R_1 =R$$ and $$R_2=\infty$$Hence $$\dfrac {1}{f}=\dfrac {\mu -1}{R}\Rightarrow f=\dfrac {R}{\mu -1}$$Speed of light in medium of lens $$v=2\times 10^8 m/s$$$$\Rightarrow \mu =\dfrac {c}{v}=\dfrac {3\times 10^8}{2\times 10^8}=\dfrac {3}{2}=1.5$$If $$r$$ is the radius and $$y$$ is the thickness of lens, the radius of curvature $$R$$ of its curved surface in accordance with the figure is given by$$R^2=r^2+(R-y)^2\Rightarrow r^2+y^2-2Ry=0$$Neglecting $$y^2; we get$$R=\dfrac {r^2}{2y}=\dfrac {(6/2)^2}{2\times 0.3}=15\ cm$$Hence$$f=\dfrac {15}{1.5-1}=30\ cmPhysics

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