Diameter of plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is $2 \times 1 0^{8} m / s$ , the focal length of the lens is:

Question

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Answer 1

The lens is as shown in the figure.

To determine the radius of curvature $R$ of the curved surface, we can write

$R^{2} = 3^{2} + (R - \frac{3}{1 0})^{2}$

Solving this, we get

$R = 15.15 c m$

Speed of light in any medium is $\frac{c}{μ}$ where $c = 3 \times 1 0^{8} m / s$ and $μ$ is the refractive index.

For the lens, $\frac{c}{μ} = 2 \times 1 0^{8} m / s$

$μ = \frac{3 \times 1 0 ^{8}}{2 \times 1 0 ^{8}} = 1.5$

Putting these values in the lens makers formula for plano convex lens, we have,

$\frac{1}{f} = (μ - 1) (\frac{1}{R}) = (1.5 - 1) (\frac{1}{1 5 . 1 5}) c m^{- 1}$

Solving this, we get $f \approx 30 c m$

Answer 2

The lens is as shown in the figure.

To determine the radius of curvature

R

of the curved surface, we can write

R^{2} = 3^{2} + (R - \frac{3}{1 0})^{2}

Solving this, we get

R = 15.15 c m

Speed of light in any medium is

\frac{c}{μ}

where

c = 3 \times 1 0^{8} m / s

and

μ

is the refractive index.

For the lens,

\frac{c}{μ} = 2 \times 1 0^{8} m / s

μ = \frac{3 \times 1 0 ^{8}}{2 \times 1 0 ^{8}} = 1.5

Putting these values in the lens makers formula for plano convex lens, we have,

\frac{1}{f} = (μ - 1) (\frac{1}{R}) = (1.5 - 1) (\frac{1}{1 5 . 1 5}) c m^{- 1}

Solving this, we get

f \approx 30 c m