Material A has critical angle iA, and material B has critical angle iB(iB iA). Then which of the following is true: (i) Light can be totally internally reflected when it passes from B to A (ii) Light can be totally internally reflected when it passes from A to B (iii) Critical angle for total internal reflection is iB-iA (iv) Critical angle between A and B is sin -1( beginarrayll sin iA sin iB endarray)

Question

Material A has critical angle iA, and material B has critical angle iB(iB > iA). Then which of the following is true: (i) Light can be totally internally reflected when it passes from B to A (ii) Light can be totally internally reflected when it passes from A to B (iii) Critical angle for total internal reflection is iB-iA (iv) Critical angle between A and B is sin -1( beginarrayll sin iA sin iB endarray) (A) (i) and (iii) (B) (i) and (iv) (C) (ii) and (iii) (D) (ii) and (iv)

Tardigrade Admin · Accepted Answer

iB>iA⇒ medium A is denser μ A=(1/sin iA) and μ B=(1/sin iB) Also <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-rttdk3ttouh0kdif.jpg" /> θC= sin -1 ((μB/μA)) or θC= sin -1( beginarrayll( sin /) iA sin iB endarray)

(i) and (iii)

(i) and (iv)

(ii) and (iii)

(ii) and (iv)

iB​>iA​⇒ medium A is denser μA​=siniA​1​ and μB​=siniB​1​ Also θC​=sin−1(μA​μB​​) or θC​=sin−1(sin​iA​sin​iB​​)

$i_{B} > i_{A} \Rightarrow$ medium $A$ is denser
$μ_{A} = \frac{1}{s in i _{A}}$ and $μ_{B} = \frac{1}{s in i _{B}}$
Also

$θ_{C} = sin^{- 1} (\frac{μ _{B}}{μ _{A}})$
or $θ_{C} = sin^{- 1} (s i n i_{A} sin i_{B})$