SATHEE: Optics 7 Question 10

Optics 7 Question 10

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

(2013 Main)

(a) $15 c m$

(b) $20 c m$

(d) $10 c m$

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Solution:

By Pythagoras theorem

$R^{2} = (3)^{2} + (R - 0.3)^{2} \Rightarrow R \approx 15 c m$

Refractive index of material of lens $μ = \frac{c}{v}$

Here $c =$ speed of light in vacuum $= 3 \times 10^{8} m / s$

$v =$ speed of light in material of lens $= 2 \times 10^{8} m / s$

$= \frac{3 \times 10^{8}}{2 \times 10^{8}} = \frac{3}{2}$

From lens maker’s formula

$\frac{1}{f} = (μ - 1) \frac{1}{R_{1}} - \frac{1}{R_{2}}$

Here, $R_{1} = R$ and $R_{2} = \infty$ (For plane surface)

$\begin{aligned} \frac{1}{f} = \frac{3}{2} - 1 \frac{1}{15} \\ \Rightarrow & f & = 30 c m \end{aligned}$

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Optics 7 Question 10

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

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