First slide

Ray optics

Question

Diameter of a plano - convex lens is 6 cm and its thickness at the centre is 3 mm. Then the focal length of the lens, if the speed of light in the material of lens is 2 × 10⁸ m/s

Moderate

A

7.5 cm
B

15 cm
C

45 cm
D

30 cm

Solution

$μ = \frac{c}{v}, μ = \frac{3 x 10^{8}}{2 x 10^{8}} = 1.5$ For plano covex lens
$\frac{1}{f} = \frac{(μ - 1)}{R}, f = \frac{R}{(μ - 1)}; R^{2} = r^{2} + {(R - y)}^{2}$
( $∴$ Neglecting y²)
$R = \frac{r^{2}}{2 y} \Rightarrow R = \frac{9 x 10^{- 4}}{2 x 3 x 10^{- 3}} = 0.15 m; R = 15 cm Focal length f = \frac{15}{(1.5 - 1)} = 30 cm$

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