Question

A vertical pencil rays comes from bottom of a tank filled with a liquid. When tank is accelerated with acceleration of 7.5 m/s² the ray is seen to be just totally reflected by liquid surface. What is true about refractive index of liquid i.e. about m -

• A. m slightly greater than $\frac { 4 } { 3 }$
• B. m slightly greater than $\frac { 5 } { 3 }$
• C. m slightly greater than 1.5
• D. m slightly greater than 1.75

Answer 1

Answer: (B)

m slightly greater than $\frac { 5 } { 3 }$

Answer 2

F₁ – F₂ = ma

rg [h₁ – h₂] × A = a × r A L

tan q = $\frac { \mathrm { h } _ { 1 } - \mathrm { h } _ { 2 } } { \mathrm {~L} }$ = $\frac { \mathrm { a } } { \mathrm { g } }$

q > q_c [Total internal reflection]

tan q > tan q_c

$\frac { \mathrm { a } } { \mathrm { g } }$> tan q_c

sin q = $\frac { 1 } { \mu }$

$\frac { 75 } { 100 }$ > $\frac { 1 } { \sqrt { \mu ^ { 2 } - 1 } }$

9 (m² – 1) > 16

9m² > 16 + 9

m > $\frac { 5 } { 3 }$