First slide

Ray optics

Question

Two identical glass $(μ_{g} = \frac{3}{2})$ equiconvex lenses of focal length f each are kept in contact. The space between the two lenses is filled with water $(μ_{w} = \frac{4}{3})$ . The focal length of the combination is

Moderate

A

$\frac{f}{3}$
B

f
C

$\frac{4 f}{3}$
D

$\frac{3 f}{4}$

Solution

water between two convex lenses can be considered as a concave lens.So,
$\frac{1}{f} = \frac{(μ_{g} - 1) \times 2}{R} = \frac{1}{R}$
for concave lens $p o w e r = \frac{1}{f_{1}} = (μ_{w a t e r} - 1) (- \frac{2}{R}) = - \frac{2}{3 f}$
solving both the equation $f_{e q} = \frac{3 f}{4}$

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