The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and one-third the size of the object. The wavelength of light inside the lens is times the wavelength in free space. The radius of the curved surface of t

Question

The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and one-third the size of the object. The wavelength of light inside the lens is $\frac{2}{3}$ times the wavelength in free space. The radius of the curved surface of the lens is [2013]

Smart Achievers · Accepted Answer

(3)

Here, $μ = \frac{λ_{air}}{λ_{medium}} = \frac{1}{\frac{2}{3}} = \frac{3}{2} = 1.5$

Also, $m = \frac{v}{u} = - \frac{1}{3}$ $(∵ v = 8 m)$ $∴$ $u = - 24 cm$

For a plano-convex lens,

$\frac{1}{f} = \frac{μ - 1}{R} = \frac{1}{v} - \frac{1}{u}$ or $\frac{1.5 - 1}{R} = \frac{1}{8} - (\frac{1}{- 24}) = \frac{1}{8} + \frac{1}{24} = \frac{1}{6}$

$∴$ $R = 3 m$

Solution

Q.
The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and one-third the size of the object. The wavelength of light inside the lens is $\frac{2}{3}$ times the wavelength in free space. The radius of the curved surface of the lens is [2013]

1 1 m

2 2 m

3 3 m

4 6 m

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