Question

Diameter of a plano–convex lens is 6 cm. and its thickness at the centre is 3 mm. What is the focal length of the lens. If the speed of light in the material of lens is 2 × 108 m/s :-
(1) 30 cm
(2) 20 cm
(3) 10 cm
(4) 40 cm

Answer 1

Answer on Question #42273-Physics-Optics

Diameter of a plane-convex lens is $6\mathrm{cm}$ . and its thickness at the center is $3\mathrm{mm}$ . What is the focal length of the lens? If the speed of light in the material of lens is $2\times 108~\mathrm{m / s}$ :-

(1) $30\mathrm{cm}$ (2) $20\mathrm{cm}$ (3) $10\mathrm{cm}$ (4) $40\mathrm{cm}$

Solution

$v = 2\cdot 10^{8}\frac{m}{s},c = 3\cdot 10^{8}\frac{m}{s},\mu = \frac{c}{v} = 1.5,D = 6cm = 60mm,R = \frac{D}{2} = 30mm.$

Here we have to find the radius of the surface of the lens. $O$ is the center of the circle. So AC is the chord of the circle. By Pythagoras's theorem

$$R ^ {2} = 3 0 ^ {2} + (R - 3) ^ {2} \rightarrow R ^ {2} = 9 0 0 + R ^ {2} - 6 R + 9 \rightarrow R = 1 5 c m.$$

By lens makers formula for a plane-convex lens

$$\frac {1}{f} = (\mu - 1) \cdot \frac {1}{R} \rightarrow f = \frac {R}{(\mu - 1)} = \frac {1 5 c m}{1 . 5 - 1} = 3 0 c m.$$

Answer: $30~\mathrm{cm}$

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