The critical angle of a medium B with respect another medium A is 45 $^{\circ}$ and the critical angle of a medium C with respect the medium B is 30 $^{\circ}$ . The critical angle of medium C with respect to A is :
Less than 30 $^{\circ}$
Greater than 30 $^{\circ}$
Cannot be determined
30 $^{\circ}$

Question

The critical angle of a medium B with respect another medium A is 45 $^{\circ}$ and the critical angle of a medium C with respect the medium B is 30 $^{\circ}$ . The critical angle of medium C with respect to A is :
Less than 30 $^{\circ}$
Greater than 30 $^{\circ}$
Cannot be determined
30 $^{\circ}$

Toppr Admin · Accepted Answer

-x3BC-Bsin45-x2218-x3BC-A-x3BC-Csin30-x2218-x3BC-B-x3BC-Csin30sin45-x3BC-A-x3BC-C12-x221A-2-x3BC-A-x2234-critical-xA0-angle-sin-x2212-1-12-x221A-2-lt-30-x2218-

The critical angle of a medium B with respect another medium A is 45∘ and the critical angle of a medium C with respect the medium B is 30∘. The critical angle of medium C with respect to A is :Less than 30∘Greater than 30∘Cannot be determined30∘

μBsin45∘=μAμCsin30∘=μBμCsin30sin45=μAμC12√2=μA∴critical angle=sin−1(12√2)<30∘

$μ_{B} s i n 45^{\circ} = μ_{A}$

$μ_{C} s i n 30^{\circ} = μ_{B}$

$μ_{C} s i n 30 s i n 45 = μ_{A}$

$μ_{C} \frac{1}{2 \sqrt{2}} = μ A$

$∴ c r i t i c a l a n g l e = s i n^{- 1} (\frac{1}{2 \sqrt{2}}) < 30^{\circ}$