Question

A long cylindrical tube containing water is closed by an equal convex lens of focal length 10 cm in air. A point source is placed along the axis of the tube outside it at a distance 21 cm from lens. Where is the image formed? ($\mu$ of glass = 1.5)

• A. 50 cm inside the tube
• B. 70 cm inside the tube
• C. 60 cm inside the tube
• D. 55 cm inside the tube

Answer 1

Answer: (B)

First we determine the radius of spherical surface of lens:-

We know that:-

$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$

$⟹\frac{1}{f}=(\mu -1)\frac{2}{R}$

$⟹R=2(\mu -1)f$

$⟹R=2(1.5-1)\times 10=10cm$

Now, refraction at left surface:-

$\frac{\mu }{v}-\frac{{\mu }_1}{u}=\frac{\mu -{\mu }_1}{R}$

$⟹\frac{1.5}{v}-\frac{1}{-21}=\frac{1.5-1}{10}$

$\frac{1.5}{v}=\frac{1}{20}-\frac{1}{21}=\frac{1}{420}$

$⟹v=630cm$

This $v$ serves as $u$ for refraction at right surface of lens:-

Now:-

$\frac{{\mu }_2}{v}-\frac{\mu }{u}=\frac{{\mu }_2-\mu }{R}$

$⟹\frac{4/3}{v}-\frac{1.5}{630}=\frac{4/3-1.5}{-10}$

$⟹\frac{4}{3v}-\frac{1}{420}=\frac{1}{60}$

$⟹\frac{4}{3v}=\frac{1}{420}+\frac{1}{60}=\frac{8}{420}$

$⟹v=70cm$

Hence, answer is option-(A).