First slide

The lens

Question

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

Moderate

A

1 m
B

2 m
C

3 m
D

6 m

Solution

$μ = \frac{λ_{a i r}}{λ_{m e d i u m}} = \frac{1}{(2 / 3)} = \frac{3}{2} F u r t h e r, |m| = \frac{1}{3} = |\frac{v}{u}| ∴ |v| = \frac{|u|}{3}$
$v = + 8 m$ (Real image ) Given
$\Rightarrow u = - 24 m$ (Real object)

Now, $\frac{1}{v} - \frac{1}{u} = \frac{1}{f} = (μ - 1) (\frac{1}{+ R} - \frac{1}{\infty})$
$∴ \frac{1}{8} + \frac{1}{24} = (\frac{3}{2} - 1) (\frac{1}{R}) ∴ R = 3 m$

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