Question

A capillary tube is made of glass with the index of refraction 3, outer radius of the tube is 30 cm. The tube is filled with a liquid with the index of refraction 2. What should be the minimum internal radius of the tube r so that any ray that hits the tube would enter the liquid –

• A. 15 cm
• B. 10 cm
• C. 20 cm
• D. 45 cm

Answer 1

Answer: (A)

15 cm

Answer 2

q < q _c

sinq < sinq_c

sin q < $\frac { \mu _ { 1 } } { \mu _ { 2 } }$

sinq < $\frac { 2 } { 3 }$

when i is maximum q is also max and if

sinq_max < $\frac { 2 } { 3 }$ light will enter in liquid.

i_max = $\frac { \pi } { 2 }$ sin f = $\frac { 1 } { \mu _ { 2 } }$ = $\frac { 1 } { 3 }$

Apply sine rule = $\frac { \sin ( \pi - \theta ) } { R }$ = $\frac { \sin \theta } { \mathrm { R } }$

$\frac { \sin \phi } { r }$ =

$\frac { R } { 3 r }$ = sinq < $\frac { 2 } { 3 }$ r > r > $\frac { 30 } { 2 }$ r > 15 cm

minimum radius = 15 cm