Refraction by Spherical Lenses and Image Formation for CBSE Class 10

Just as spherical mirrors bounce light to form images through reflection, transparent curved glass blocks bend light to form images through refraction. From eyeglasses correcting human vision and microscopes peering into cellular life, to telescopes gazing at distant galaxies and cameras capturing moments in time, our visual world depends on lenses.

In CBSE Class 10 Science, Chapter 9 (Light - Reflection and Refraction) covers the optical behavior of convex and concave lenses, the three standard ray-tracing rules, and the complete spectrum of image formation ray diagrams.

What You Will Learn

• Definition of a spherical lens: Convex (converging) vs. Concave (diverging)
• Essential lens terminology: Optical center ($O$), Principal axis, and Principal foci ($F_1, F_2$)
• Why lenses have two foci while mirrors have only one
• The three standard ray-tracing rules for lenses
• Complete ray diagrams for all 6 object positions of a convex lens
• Ray diagrams for concave lenses
• Board exam ray diagram guidelines and common student errors

1. What is a Spherical Lens?

Definition

A spherical lens is an optically transparent medium bounded by two surfaces, of which at least one, or both, are spherical.

       Double Convex Lens (Converging)              Double Concave Lens (Diverging)
                     |                                             ) (
                    / \                                           (   )
                   |   |  Thicker in middle,                       ) (   Thinner in middle,
                    \ /   thinner at edges                        (   )  thicker at edges
                     |                                             ) (

1. Convex Lens (Double Convex / Converging Lens):
   • Bounded by two spherical surfaces bulging outwards.
   • Thicker at the center than at the edges.
   • Converges a parallel beam of light rays to a real focus point.
2. Concave Lens (Double Concave / Diverging Lens):
   • Bounded by two spherical surfaces curved inwards.
   • Thinner at the center than at the edges.
   • Diverges a parallel beam of light rays away from a virtual focus point.

2. Terminology of Spherical Lenses

Because a lens has two spherical surfaces, it has two centers of curvature and two foci:

                            Principal Axis
    ----- 2F1 --------- F1 --------- O --------- F2 --------- 2F2 -----
                           Optical Center

1. Optical Center ($O$): The central point of a lens. A ray of light passing through the optical center travels straight through without suffering any deviation.
2. Principal Axis: The imaginary straight line passing through the two centers of curvature of the lens.
3. Principal Foci ($F_1$ and $F_2$):
   • A beam of light parallel to the principal axis passing through a convex lens converges to a point on the opposite side called the second principal focus ($F_2$).
   • For a concave lens, parallel rays diverge and appear to originate from the first principal focus ($F_1$) on the same side.
4. Focal Length ($f$): The distance between the optical center ($O$) and the principal focus. By symmetry, the distance to both foci is equal ($OF_1 = OF_2 = f$).

3. The Three Standard Ray-Tracing Rules for Lenses

To locate the image formed by a lens, we trace the paths of at least two rays from the top of the object:

    Rule 1: Ray parallel to axis ----------> Refracts through Focus F2 (Convex)
    Rule 2: Ray passing through F1 --------> Refracts parallel to axis
    Rule 3: Ray passing through Center O ---> Travels straight WITHOUT ANY DEVIATION!

1. Rule 1: A ray of light from the object parallel to the principal axis passes through the principal focus $F_2$ after refraction (in a convex lens), or appears to diverge from focus $F_1$ (in a concave lens).
2. Rule 2: A ray of light passing through the principal focus $F_1$ emerges parallel to the principal axis after refraction.
3. Rule 3: <u>A ray of light passing through the optical center ($O$) of a lens emerges without suffering any deviation! This is the simplest and cleanest ray to draw in all board exam diagrams.</u>

4. Image Formation by a Convex Lens (The 6 Positions)

Important: <u>Case 6 is the hallmark of the magnifying glass! When an object (like small book text) is held close to a convex lens between the optical center and the focus ($u < f$), an upright, enlarged, virtual image is formed on the same side of the lens.</u>

5. Image Formation by a Concave Lens

A concave lens always diverges light rays, producing an image that is always virtual, erect, and diminished, situated between the optical center $O$ and focus $F_1$ on the same side as the object:

• Application: Used in spectacles to correct Myopia (nearsightedness) by diverging light rays before they enter the eye.

6. Summary and Examination Tips

Exam Tip: When drawing lens ray diagrams in board exams, ALWAYS draw Ray 3 (passing through optical center $O$ in a straight line) as your first ray! It requires no bending calculation and immediately establishes the geometric alignment for the second ray.

Common Mistake: Confusing $2F_1$ with the center of curvature. In mirrors, we write $C$; in lenses, we designate the points as $2F_1$ and $2F_2$ (twice the focal length).