REFRACTION AT SPHERICAL SURFACE

When light strikes a spherical (curved) surface, the position of object (O), the image (I) and the radius of curvature (R) are related as:

Consider another case, a spherical surface of radius R separating two media with refractive indices  . The radius of curative R will be taken positive when incident rays strike the convex side of the surface. If u is the object distance and v is the image distance,

Illustration 4:    A transparent rod 40 cm long is cut flat at one end and rounded to a hemispherical surface of 12 cm radius at the other end. A small object is embedded with in the rod along its axis and half way between its ends. When viewed from the flat end of the rod, the object appears 12.5 cm deep. What is its apparent depth when viewed from the curved end?

Solution:    For the flat surface:

Real depth of the object = 20 cm
Apparent depth = 12.5 cm
Using  m = real depth / apparent depth
             m = 20 /  12.5 = 1.6

For the curved surface:

Hence the object appears 33.3 cm deep from the curved side.