A narrow beam of light passing through the hemisphere of material with refractive index n, intersects at point O. Where does the beam converge (i.e. y in cm) if beam were to travel in the opposite direction as shown in figure(b)? The value of x is given to be 10 cm. Radius of the hemisphere is also 10 cm :-

Question

G1 Physics · Accepted Answer

Derived solution: Step 1: For paraxial refraction at a spherical surface use n₂/v - n₁/u = (n₂ - n₁)/R, applying the Cartesian sign convention at each surface. Step 2: Substitute the values given in the question and apply the geometry/sign convention shown. Step 3: On simplification the result is 5. Therefore the correct option is C.