Question 208: Wave Optics

Question

Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are 2.8 (medium $$-1$$) and 6.8 (medium $$-2$$), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be $${	an ^{ - 1}}{\left( {1 + {{10} \over 	heta }} ight)^{{1 \over 2}}}$$ the value of $$	heta$$ is __________.
(Given for dielectric media, $$\mu_r=1$$)

Accepted Answer

We know that
$$	an {	heta _0} = {{{\mu _2}} \over {{\mu _1}}}$$
$$	an {	heta _0} = \sqrt {{{6.8} \over {2.8}}}  = \sqrt {{{17} \over 7}} $$
$${	heta _0} = {	an ^{ - 1}}\sqrt {1 + {{10} \over 7}}  \Rightarrow 	heta  = 7$$

Wave Optics

Integer / Numeric Answer Type