Recall that visible light of a single frequency is described as monochromatic

3.2.3 Thin Lenses

Learning Objective

Recall that visible light of a single frequency is described as monochromatic.

Key Definitions

• Thin lens: A lens whose thickness is small compared with its focal length and the distances of the object and image from the lens.
• Convex (converging) lens: A lens that is thicker in the centre than at the edges; it converges parallel rays to a real focus.
• Concave (diverging) lens: A lens that is thinner in the centre than at the edges; it diverges parallel rays as if they originated from a virtual focus.
• Monochromatic light: Light consisting of a single frequency (or wavelength). In experiments with lenses, monochromatic light produces sharp, well‑defined images.

Lens Formula and Sign Convention

The relationship between object distance (\$u\$), image distance (\$v\$) and focal length (\$f\$) for a thin lens is given by:

\$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\$

Sign convention (Cartesian):

• Distances measured in the direction of the incident light are positive.
• Distances measured opposite to the incident light are negative.
• For a convex lens, \$f\$ is positive; for a concave lens, \$f\$ is negative.

Ray Diagram Construction

To locate the image formed by a thin lens, draw at least two of the following rays from the top of the object:

1. Parallel ray – travels parallel to the principal axis, then refracts through the focal point on the opposite side.
2. Focal ray – passes through the focal point on the object side, then emerges parallel to the principal axis.
3. Central ray – passes through the centre of the lens and continues undeviated.

Monochromatic Light and Image Quality

When a lens is illuminated with monochromatic light:

• Chromatic aberration is eliminated because all rays have the same wavelength.
• The image edges are sharp, allowing accurate measurement of image distance and magnification.
• It is ideal for laboratory investigations of the lens formula and focal length.

Comparison of Convex and Concave Lenses

Practical Example: Determining Focal Length with Monochromatic Light

Set‑up:

1. Place a distant monochromatic source (e.g., a laser pointer with a diffuser) so that the light reaching the lens is effectively parallel.
2. Position a screen on the opposite side of the lens and move it until a sharp spot of light is formed.
3. The distance from the lens to the screen is the focal length \$f\$ (positive for a convex lens).

Common Misconceptions

• “All lenses produce real images.” – Concave lenses always produce virtual images.
• “Monochromatic light is the same as white light.” – White light contains many frequencies; monochromatic light contains only one.
• “The lens formula works only for convex lenses.” – It applies to both convex and concave lenses when sign conventions are observed.

Summary

Thin lenses obey the lens formula \$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\$ with a clear sign convention. Using monochromatic light removes chromatic aberration, giving sharp images that aid in accurate measurements. Understanding the differences between convex and concave lenses, and correctly applying ray diagrams, are essential skills for the IGCSE Physics syllabus.

Practice Questions

1. A convex lens has a focal length of \$+12\ \text{cm}\$. An object is placed \$18\ \text{cm}\$ from the lens. Calculate the image distance and state the nature of the image.
2. Explain why a monochromatic light source is preferred when measuring the focal length of a lens in a laboratory.
3. Draw a ray diagram (describe the steps) for a concave lens forming an image of an object placed \$30\ \text{cm}\$ from the lens with a focal length of \$-10\ \text{cm}\$.