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# Ray Diagram of Spherical Lenses | Diagram and Explanation

## Ray Diagram of Spherical Lenses

### Introduction

We know that the spherical mirrors form various kind of images such as real, virtual, magnified, diminished, same sized, point sized etc. Previously, we learnt how to locate the images formed due to the spherical mirrors, by drawing ray diagrams. Spherical lenses as well form such images which can be located by drawing ray diagrams. It is always convenient to choose the incident ray whose corresponding refracted ray is known to locate the images.

### Refraction through spherical lenses:

A lens is a transparent object which lets light pass through it. However, a light ray bends at each refractive interface because of refraction.

A lens has two refractive interfaces viz., air-glass interface (1) and glass-air interface (2).

Interface 1 (Air-glass):

Here, the light ray enters a denser medium (glass) from a rarer medium (air). Therefore, it bends towards the normal on refraction.

Interface 2 (Glass-air):

Here, the light ray enters a rarer medium (air) from a denser medium (glass). Therefore, it bends away from the normal on refraction.

All the light rays in a parallel beam of light undergo two refractions to finally converge to a point called the focus.

### Assumptions for drawing ray diagrams:

Consider an extended object of finite size, placed in front of a spherical lens. It is usually denoted by an arrow as shown.

An infinite number of light rays originate from each small portion of this object.

However, it would be convenient to choose either 2 or 3 of the rays so that the ray diagram is clear.

For each ray incident on the lens, the corresponding refracted ray needs to be drawn in order to locate the image.

### Predictable refracted rays:

Usually, 2 or 3 incident rays are chosen for a particular point on the object in such a way that the refracted rays corresponding to them are known. This is because the image is formed at the point of intersection of the refracted rays.

A light ray parallel to the principal axis:

• Passes through the principal focus after refraction through a convex lens.
• Appears to diverge from the principal focus after refraction through a concave lens.

An incident ray passing through the principal focus of a convex lens emerges parallel to the principal axis after refraction through a convex lens.

An incident ray approaching the principal focus of a concave lens emerges parallel to the principal focus after refraction through a concave lens.

A ray of light passing though the optical center of a lens (convex and concave) emerges without any deviation from its original path.

## Summary

• A lens is a transparent object which lets light pass through it. However, a light ray
bends at each refractive interface.
• A lens has two refractive interfaces viz., air-glass interface and glass-air interface.
• A light ray bends towards the normal while getting refracted through the air-glass interface and away from the normal while getting refracted through the glass-air
interface.
• The images formed by spherical lenses are located by drawing ray diagrams.
• While drawing ray diagrams the incident rays should be chosen so that their
corresponding refracted rays are predictable.
• The image of a point on the extended object is formed at the point of intersection of at
least two refracted rays corresponding to the incident rays originating from that point.
• An incident ray parallel to the principal axis passes through the focus after refraction
by a convex lens.
• An incident ray parallel to the principal axis appears to diverge from the focus after refraction by a concave lens.
• An incident ray passing through the focus goes parallel to the principal axis after refraction by a convex lens.
• An incident ray heading towards the focus goes parallel to the principal axis after
refraction by a concave lens.
• An incident ray passing through the optical center emerges undeviated from its actual
path after refraction through both concave and convex lenses.

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