A uniform horizontal beam of light is incident upon a quarter cyclinder of radius R=5cm, and has a refractive index 2//sqrt3, A patch on the table at a distance x from the cylinder is unilluminated. Find the value of x?

A uniform horizontal beam of light is incident upon a quarter cyclinde

1.	A uniform horizontal beam of light is incident upon a quarter cyclinder of radius R=5cm, and has a refractive index 2//sqrt3, A patch on the table at a distance x from the cylinder is unilluminated. Find the value of x?
Answer» Solution :When the angle of incidence is `theta_c` x region will remain unilluminated. This is the limiting CASE. When the angle of incidence is greater than critical agle TIR will place In this case, also x regio is unilluminated. When angle of incidence `THETA lt theta_c` then the incident ray will REFRACT and hence x region will be illuminated. So in limiting case: In `Delta PQR, cos theta_c= R/(R+x) sin theta_c= mu_r/mu_d=1/(2//sqrt3)=sqrt3/2` `therefore theta_c=60^@, R=5cm` (GIVEN) `IMPLIES cos 60=5/(5+x) implies 5+x=10 implies x=5cm`