Question

How does a light ray proceed in a lens? Show by a diagram.

Hint:

Sign convention (real is positive to the right of lens): \( \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \), \( m=\frac{v}{u}=\frac{h_i}{h_o} \).

Answer 1

Light refracts at both surfaces of a thin lens.

Key Rules:

1. A ray parallel to the principal axis passes through the focal point of a convex lens (or appears to diverge from the focus of a concave lens).
2. A ray through the optical center travels undeviated.
3. A ray directed toward the focus emerges parallel to the axis.

Image position and size follow from the lens formula:

\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]

and magnification:

\[ m = \frac{v}{u} \]

Step 1: Refraction at a Thin Lens.
Using the small-angle (paraxial) approximation, a lens redirects rays according to Snell’s law at each surface. For a convex lens, rays converge; for a concave lens, rays diverge.

Step 2: Principal Rays (Construction).
To locate images quickly:

• Parallel ray → passes through \( F \) (convex) / appears from \( F \) (concave).
• Central ray → through optical center \( O \), undeviated.
• Focal ray → aimed at \( F \), emerges parallel to the axis.

Step 3: Nature of Images.

• Convex Lens:
  • Object beyond \( 2F \): real, inverted, diminished (image between \( F \) and \( 2F \)).
  • Object at \( 2F \): real, inverted, same size (image at \( 2F \)).
  • Object between \( F \) and \( 2F \): real, inverted, magnified (image beyond \( 2F \)).
  • Object inside \( F \): virtual, erect, magnified (image on same side).
• Concave Lens: always forms virtual, erect, and diminished images.