Refraction of light by spherical lenses

Refraction of light by spherical lenses is an essential concept in optics for Class 10 NCERT. Spherical lenses are transparent materials with at least one curved surface that cause light rays to bend or refract. They are primarily categorized into two types:

1. Convex Lenses (Converging Lenses)
2. Concave Lenses (Diverging Lenses)

Basic Terminology

1. Optical Center (O): The central point of the lens.
2. Principal Axis: The straight line passing through the optical center and perpendicular to the surfaces of the lens.
3. Focus (F): The point where light rays parallel to the principal axis converge (convex) or appear to diverge from (concave) after refraction.
4. Focal Length (f): The distance between the optical center and the focus.
5. Principal Focus (F1 and F2): Convex lenses have two principal foci, one on each side. Concave lenses also have two principal foci, but rays appear to diverge from them.

Refraction in Convex Lenses

Convex lenses are thicker at the center than at the edges and converge light rays passing through them. Here’s how image formation works with convex lenses based on the object’s position relative to the lens.

1. Object at Infinity: Parallel rays converge at the focus (F) on the other side.
   • At F, real, inverted, and highly diminished.
2. Object Beyond 2F: Rays converge between F and 2F.
   • Between F and 2F, real, inverted, and diminished.
3. Object at 2F: Rays converge at 2F on the other side.
   • At 2F, real, inverted, and same size.
4. Object Between F and 2F: Rays converge beyond 2F.
   • Beyond 2F, real, inverted, and magnified.
5. Object at F: Rays become parallel after passing through the lens.
   • At infinity, real, inverted, and highly magnified.
6. Object Between F and O: Rays diverge, and when extended backward, appear to come from a point on the same side of the lens.
   • On the same side as the object, virtual, erect, and magnified.

Refraction in Concave Lenses

Concave lenses are thinner at the center than at the edges and diverge light rays passing through them. Image formation in concave lenses is simpler as they always form virtual, erect, and diminished images regardless of the object’s position.

1. Object at Infinity: Parallel rays appear to diverge from the focus (F) on the same side.
   • At F, virtual, erect, and highly diminished.
2. Object at Finite Distance: Rays appear to diverge from a point between F and O on the same side.
   • Between F and O, virtual, erect, and diminished.

Ray Diagrams

Drawing ray diagrams helps in visualizing how lenses form images:

1. For Convex Lenses:
   • A ray parallel to the principal axis passes through the focus on the other side.
   • A ray passing through the optical center goes straight without bending.
   • A ray passing through (or directed towards) the focus on the object side emerges parallel to the principal axis.
2. For Concave Lenses:
   • A ray parallel to the principal axis appears to diverge from the focus on the same side.
   • A ray passing through the optical center goes straight without bending.
   • A ray directed towards the focus on the other side emerges parallel to the principal axis.

Lens Formula and Magnification

For lenses, the relationship between the object distance (u), the image distance (v), and the focal length (f) is given by the Lens Formula: 1f=1v−1u\frac{1}{f} = \frac{1}{v} – \frac{1}{u}f1​=v1​−u1​

Magnification (m) is the ratio of the height of the image (h’) to the height of the object (h): m=h′h=vum = \frac{h’}{h} = \frac{v}{u}m=hh′​=uv​

For convex lenses, magnification can be positive or negative depending on the nature of the image (real or virtual). For concave lenses, magnification is always positive since the image is always virtual and erect.

Understanding these principles helps in solving problems related to image formation by lenses and comprehending the fundamental behavior of light as it passes through different optical mediums.