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. Using monochromatic light with thin lenses removes chromatic aberration, giving sharp, well‑defined images that can be measured accurately.

Core Syllabus Requirement

Describe the action of thin converging & diverging lenses on a parallel beam of light.

Answer (to be included in the notes): A parallel beam incident on a converging (convex) lens is refracted so that the rays meet at the principal (real) focus on the far side of the lens. A parallel beam incident on a diverging (concave) lens is refracted as if it originated from the principal (virtual) focus on the near side of the lens.

Key Definitions (Cambridge terminology)

• Thin lens: A lens whose thickness is negligible compared with its focal length and with the object‑ and image‑distances.
• Principal axis: The straight line passing through the centre of the lens and perpendicular to its surfaces.
• Principal focus (principal focal point): The point on the principal axis where parallel rays either converge (convex lens) or appear to diverge from (concave lens). The distance from the lens centre to this point is the focal length \$f\$.
• Convex (converging) thin lens: Thicker in the centre than at the edges; it brings parallel rays to a real principal focus.
• Concave (diverging) thin lens: Thinner in the centre than at the edges; it makes parallel rays appear to diverge from a virtual principal focus.
• Monochromatic light: Light consisting of a single frequency (or wavelength). In lens experiments it produces sharp images because all rays have the same wavelength.

Lens Formula and Cartesian Sign Convention

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

Sign rules (Cartesian convention used in Cambridge exams)

• Distances measured in the direction of the incident light are taken as positive.
• Distances measured opposite to the incident light are negative.
• For a convex (converging) lens \$f\$ is positive; for a concave (diverging) lens \$f\$ is negative.

Note: Some textbooks adopt the “real‑is‑positive” convention. The Cambridge board uses the Cartesian convention above, so use it consistently in all calculations.

Worked Example – Concave Lens

Given: \$f = -8\ \text{cm}\$ (diverging lens), object distance \$u = 20\ \text{cm}\$ to the left of the lens.

1. Assign signs: \$f = -8\ \text{cm}\$ (negative), \$u = -20\ \text{cm}\$ (object is on the incident‑light side, therefore negative).
2. Insert into the lens formula:
   

   \$\frac{1}{-8}= \frac{1}{-20}+ \frac{1}{v}\$

3. Re‑arrange:
   

   \$\frac{1}{v}= \frac{1}{-8}-\frac{1}{-20}= -0.125 + 0.05 = -0.075\$

4. Hence \$v = -13.3\ \text{cm}\$ (negative ⇒ virtual image on the same side as the object).
5. Result: the image is upright, reduced, and located \$13.3\ \text{cm}\$ in front of the lens.

Ray‑Diagram Construction

To locate the image formed by a thin lens, draw any two of the three standard rays from the top of the object. The three rays are:

1. Parallel ray: Travels parallel to the principal axis, then:

   • through the principal focus on the far side of a convex lens, or
   • appears to diverge from the virtual focus on the near side of a concave lens.

2. Focal ray: Passes through the principal focus on the object side, then emerges parallel to the principal axis.
3. Central ray: Passes straight through the centre of the lens and continues undeviated.

Typical Cases to Draw

• Convex lens – real image (object beyond \$f\$): The three rays intersect on the far side of the lens; the image is inverted and can be projected on a screen.
• Convex lens – virtual image (object inside \$f\$): Extend the refracted rays backwards; they meet on the same side of the lens as the object. The image is upright, enlarged, and cannot be projected.
• Concave lens – always virtual: All refracted rays diverge; extend them backwards to locate the virtual image on the object side. The image is upright and reduced.

Monochromatic Light and Image Quality

When a lens is illuminated with monochromatic light:

• Chromatic aberration is eliminated because all rays have the same wavelength.
• Image edges are sharp, allowing accurate measurement of \$v\$ and calculation of magnification \$m = v/u\$.
• It is the preferred source for laboratory investigations of the lens formula and focal‑length determination.

Comparison of Convex and Concave Lenses

Practical Example: Determining Focal Length with Monochromatic Light

1. Set up a distant monochromatic source (e.g., a laser pointer with a diffuser) so that the light reaching the lens is effectively parallel.
2. Place a white screen on the opposite side of the lens.
3. Move the screen until a sharp, circular spot of light is obtained. The distance between lens and screen is the focal length \$f\$ (positive for a convex lens; for a concave lens the virtual focus can be measured by tracing the diverging rays backward).
4. Record the measurement, repeat several times, and take the average.

Common Misconceptions

• “All lenses produce real images.” – Concave lenses always produce virtual, upright images.
• “Monochromatic light is the same as white light.” – White light contains many frequencies; monochromatic light contains only one, eliminating colour‑dependent focal shifts.
• “The lens formula only works for convex lenses.” – It applies to both convex and concave lenses when the correct sign convention is used.
• “If the object is within the focal length of a convex lens, no image forms.” – A virtual, upright, enlarged image does form; it simply cannot be projected onto a screen.

Summary

Thin lenses obey the Cartesian lens formula

with clear sign rules: distances measured in the direction of incident light are positive, opposite directions are negative; \$f\$ is positive for converging lenses and negative for diverging lenses. Using the exact syllabus terms – principal axis, principal focus, focal length – reinforces terminology. Monochromatic light removes chromatic aberration, giving sharp images that enable precise measurements. Mastery of ray‑diagram construction (including the explicit action on parallel beams) and correct sign‑convention usage is essential for success in the Cambridge IGCSE Physics 0625 examination.

Practice Questions

1. Calculation: A convex lens has a focal length of \$+12\ \text{cm}\$. An object is placed \$18\ \text{cm}\$ from the lens. Find the image distance and state the nature of the image.
2. Conceptual: Explain why a monochromatic light source is preferred when measuring the focal length of a lens in a laboratory.
3. Ray diagram: Draw (or describe) a ray diagram for a concave lens with \$f = -10\ \text{cm}\$ and an object \$30\ \text{cm}\$ from the lens. Identify the image position, size and orientation.
4. Sign‑convention problem: Using the Cartesian sign convention, solve for the image distance when a convex lens (\$f = +8\ \text{cm}\$) forms a virtual image of an object placed \$5\ \text{cm}\$ from the lens.