Spherical Surface Refraction and Image Formation

Summary:

The Spherical Surface Refraction and Image Formation note discusses the topics of refraction by spherical surfaces and image formation. It starts by explaining refraction at spherical interfaces between transparent media, where the laws of refraction can be applied at each point on the surface. The text introduces the small angle approximation and discusses the relationships between angles and distances on the spherical surface.

Next, the text presents the application of Snell’s law and the derivation of equations that relate object distance, image distance, refractive indices, and the radius of curvature of the spherical surface. It emphasizes that the derived equations hold for any curved spherical surface.

The text then provides a problem-solving example related to the apparent depth of a pin viewed through a glass slab. It demonstrates the application of the refractive index and the derivation of the apparent depth based on the ratio of actual depth to refractive index.

Moving on to refraction at a plane interface, the text discusses the apparent depth phenomenon and how the refraction of light can create the illusion of bending or distortion when observing objects in different media. It explains the concept of apparent depth and provides a formula for calculating it based on the refractive indices of the two media.

The text concludes by discussing refraction at a convex surface, specifically a spherical surface. It explains the application of Snell’s law and the small-angle approximation to derive equations that relate the object distance, image distance, and radius of curvature of the convex surface.

Excerpt:

Spherical Surface Refraction and Image Formation

Refraction at Spherical Surfaces
Think about refraction at a spherical interface point between two transparent media. A microscopic piece of a round surface can be viewed as planar and similar laws of refraction can be applied at each point on the surface.

The rays are incident from a medium of refractive index n1 to another of refractive index n2. Assuming the aperture (or the lateral size) of the surface to be small compared to other distances involved a small angle approximation can be made.