Refractive index of the material of a sphere of radius 10 cm is 23. A point source of light P is placed just inside the surface of the sphere. Then area of the surface of the sphere through which light energy can pass into surrounding air, is

From the ray diagram, ∠PAC=∠PBC=θC=sin−1123=60o∴ ∠ACB=4θC=240o=4π3Therefore area of surface through area of surface through which rays of light can pass into surrounding area = Area AQB Solid angle ACB=ϕ=2π1−cos4θC2⇒ϕ=2π1−cos2×π3=2π1+12=3π radian∴ Area AQB=3π×R2=2π×102cm2=200π cm2