#### Refraction at Curved Surfaces, Physics tutorial

Introduction:

Just as reflection takes places at curved and plane surfaces, similarly, refraction can also occur at plane and curved surfaces. In the last unit, we have discussed about the refraction through a prism. In this unit we shall look at refraction at curved surfaces. Figure given above shows refraction at a curved surface.

Image Formed by Refraction at a Curved Surface:

In Figure given above, point O is the object near the convex spherical refracting surface of radius of curvature r. Surface separates two media whose indices of refraction differ, that of medium in which incident light falls on surface being m1 and that on the other side of the surface being m2.

The light source ray which enters normally at point P would pass through undeviated and pass through center of curvature. The bright ray which enters at any other angle (Q for instance) would be deviated or converged to intersect with the ray which passing through center of curvature to create the real image. If surface were concave then refracting ray would diverge and if created backwards would form the virtual image as shown in figure (b)

The object and image distance are related by the formula (here we have written only the result. The formula is not derived.)

μ1/u + μ2/v = μ2 - μ1/r................Eq.1

Where

u = object distance

v = image distance

r = radius pf curvature of surface

μ1, μ2 = refractive index of the two media

Note that m1, is refractive index of the medium in which the light is initially traveling before it gets in medium with refractive index m2.

We should use sign conventions if we are to use equation to the variety of cases. Side of surface in which light rays originate stated as front side. Other side is known as back side. Real images are formed by refraction in back of surface in contrast with mirrors, where real images are formed in front of reflecting surface. Due to difference in location of real images, refraction sign conventions for v and r are opposite reflection sign conventions. Just as in refraction image formed can be enlarged or diminished and magnification of image is provided by

m = (μ12)(v/u)

Refraction through Lenses:

Phenomenon of refraction is change in direction of the ray of light when it travels from one medium to another of different density.

Refraction through lenses involves same change in direction of light rays.

The lens is the portion of the transparent medium bounded by two spherical surfaces or by the plane and the spherical surface. The different kinds of lenses are given.

Usually, a converging or convex lens makes rays of light originating from the point come together at another point while diverging or concave lens makes rays of light that pass through the point spread out or diverge.

Major characteristics of the Lens:

The typical lens of whatever kind has major characteristics

i) The Principal Axis: This is line joining the centers of curvature of two curved surfaces forming lens.

ii) Optical Centre: For every lens there is point C through which rays of light pass through without being deviated by lens. This point is known as optical center of the.

iii) The Principal Focus: The principal focus F of the converging lens is point to which all rays parallel and close to principal axis converge after refraction through lens. Principal focus of the diverging lens is point from which all rays parallel and close to principal axis seems to diverge from after refraction through lens.

iv) Focal Length: Focal length F is distance between optical center and principal focal of the lens. Principal focus of the converging lens is on far side from the incident rays while for the diverging lens the principal focus is on same side as the incident rays and the refracted rays don't really pass through it.

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