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CBSE Class 10 Answered

Let the refractive index of a denser medium with respect to rarer medium be n12 and its critical angle angle B. At an angle of incidence A when light travels from denser medium to rarer medium, a part of light is reflected and rest is refracted and the and the angle between reflected and refracted ray is 90 degree. What is relation between A and B.   ? a) tan A = sin B b) sec A = cos B c) sin A = tan B d) cos A = sec B
Asked by acv27joy | 16 Sep, 2018, 12:36: PM
answered-by-expert Expert Answer
it can be seen from figure, if A is angle of incidence at the boundary of denser medium, then angle of refraction is (90-A)
because angle between refracted and reflected ray is 90º
 
hence we have as per law of refraction,  sin(90-A)/sin(A) = n12 ..................(1)
 
we rewrite eqn.(1) as, cot(A) = n12 ..................(2)
 
critical angle B and refractive index are related as, sin(B) = 1/n12   ...............(3)
 
from(2) and (3) we can write,     tan(A) = sin(B)
Answered by Thiyagarajan K | 16 Sep, 2018, 03:25: PM
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