question_answer

A point source of light is placed at a depth of h below the surface of water of refractive index \[\mu .\] A floating opaque disc is placed on the surface of water so that light from the sources is not visible from the surface. The minimum diameter of the disc is       

A) \[2h{{\left( {{\mu }^{2}}-1 \right)}^{1/2}}\]

B) \[2h{{\left( {{\mu }^{2}}-1 \right)}^{1/2}}\]

C) \[h/\left[ 2{{\left( {{\mu }^{2}}-1 \right)}^{1/2}} \right]\]

D) \[h/{{\left( {{\mu }^{2}}-1 \right)}^{1/2}}\]

Correct Answer: A

Solution :

[a] The figure shows incidence from water at critical angle \[{{\theta }_{c}}\] for the limiting case. Now, \[\sin {{\theta }_{c}}=1/\mu \] so that \[\tan {{\theta }_{c}}=1/{{\left( {{\mu }^{2}}-1 \right)}^{1/2}}\] which is also equal to r/h where r is the radius of the disc.    Therefore, diameter of the disc is \[2r=2h\tan {{\theta }_{c}}\]