First slide

Ray optics

Question

Two convex lenses, each of focal length 40 cm, are filled at the ends of a tube and the tube is filled with water $(μ = \frac{4}{3})$ . A beam of parallel rays parallel to the axis of the tube, enters the tube through one end and emerges from the tube as a beam of parallel rays of same diameter as the incident beam. If refractive index of glass is 1.5, find the length l of the tube.

Difficult

A

90 cm
B

80 cm
C

160 cm
D

120 cm

Solution

For each lens, if R be the radius of curvature of each convex surface, then
$\frac{1}{f} = \frac{2 (μ_{g} - 1)}{R} \Rightarrow R = 2 (1 .5 - 1) \times 40 cm \Rightarrow R = 40 cm$
If x and y be the second focal length and first focal lengths of lenses 1 and 2 respectively, then x = y.
For lens - 1,
$\frac{μ}{(+ x)} - \frac{1}{α} = \frac{μg - 1}{(+ R)} - \frac{μg - μ}{(- R)} \Rightarrow \frac{μ}{x} = \frac{2 μg - μ - 1}{R}$
$\Rightarrow \frac{4 / 3}{x} = \frac{2 \times 1 .5 - \frac{4}{3} - 1}{40} \Rightarrow x = 80 cm$
$∴ l = x + y = x + x = (80 + 80) cm = 160 cm$

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