Question

Light travels in two media A and B with speeds $1.8 \times 10 ^ { 8 } \mathrm {~ms} ^ { - 1 }$ and $2.4 \times 10 ^ { 8 } \mathrm {~ms} ^ { - 1 }$respectively. Then the critical angle between them is:

• A. $\sin ^ { - 1 } \left( \frac { 2 } { 3 } \right)$
• B. $\tan ^ { - 1 } \left( \frac { 3 } { 4 } \right)$
• C. $\tan ^ { - 1 } \left( \frac { 2 } { 3 } \right)$
• D. $\sin ^ { - 1 } \left( \frac { 3 } { 4 } \right)$

Answer 1

Answer: (D)

$\sin ^ { - 1 } \left( \frac { 3 } { 4 } \right)$

Answer 2

: Here, $\mathrm { v } _ { \mathrm { A } } = 1.8 \times 10 ^ { 8 } \mathrm {~ms} ^ { - 1 }$

Light travels slower in denser medium. Hence medium A is a denser medium and medium B is a rarer medium, Here, light travels from medium A to medium B. Let C be the critical angle between them.

Refractive index of medium B w.r.t. to medium A is

${ } ^ { \mathrm { A } } \mu _ { \mathrm { B } } = \frac { \text { Velocity of light in medium } \mathrm { A } } { \text { Velocity of light in medium } \mathrm { B } } = \frac { \mathrm { v } _ { \mathrm { A } } } { \mathrm { v } _ { \mathrm { B } } }$

or