C
CraftExam
medium difficulty10 min

Refraction at Spherical Surfaces and Lens Maker's Formula

Refraction at a spherical surface describes image formation when light passes between two media separated by a curved refracting boundary. The lens maker's formula gives the focal length of a thin lens in terms of refractive index and radii of curvature of its two surfaces.

In one line: In a usual biconvex lens with light from left, R1 is positive and R2 is negative.

Concept Practice Coming Soon

Understand it

  • For a single spherical refracting surface, the object and image distances are measured from the pole of the surface and the radius is signed using the Cartesian convention.
  • The relation connects n1, n2, u, v and R.
  • A thin lens is treated as two spherical refracting surfaces close together.
  • Combining the two refractions gives the lens maker's formula.
  • This result explains why focal length depends on lens material, surrounding medium and curvatures of the two faces.

Example

A biconvex glass lens has positive power in air because its surfaces make parallel rays converge. If placed in a medium with refractive index close to glass, its focal length increases greatly because the relative refractive index decreases.

Formula and rule

Spherical surface formula: n2/v - n1/u = (n2 - n1)/R.

Lens maker's formula for a thin lens in air: 1/f = (n - 1)(1/R1 - 1/R2).

More generally, n is the relative refractive index of lens material with respect to surrounding medium.

Distances R1, R2 and f are in metres for SI use; refractive index is dimensionless.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

For a thin biconvex glass lens in air, n = 1.5, R1 = +20 cm and R2 = -20 cm.

  1. 11/f = (1.5 - 1)(1/20 - 1/(-20)) = 0.5 × (1/20 + 1/20) = 0.5 × 1/10 = 1/20 per cm.
  2. 2Thus f = 20 cm = 0.20 m.
  3. 3The lens is converging with power +5 D.

Method you can reuse

Choose the direction of incident light; mark R signs for each surface; use relative refractive index; substitute in lens maker's formula; convert focal length to metre if power is required; interpret positive or negative f.

Visual tip

Diagram should show a spherical refracting surface, pole P, centre C, radius R, object O, image I, normal through C, and refracted ray. For a lens, mark first and second surfaces, R1, R2, optical centre and principal axis.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why does the focal length of a lens depend on the medium around it?

Think first, then show answer
A lens bends light because its refractive index differs from that of the surrounding medium. If the surrounding medium changes, the relative refractive index changes, so the bending at each surface changes and the focal length also changes.

Common wrong answer

For a biconvex lens, taking both R1 and R2 as positive gives 1/f = 0, which wrongly suggests no focusing.

Don't mix this up

Students often use the absolute refractive index of the lens without considering the surrounding medium, or assign the same sign to R1 and R2 for a biconvex lens.

Exam tip

In lens maker problems, first write the direction of incident light and decide the signs of R1 and R2 from the position of each centre of curvature.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

It is asked as derivation of lens maker's formula, radius sign questions, focal length numericals, and conceptual questions on a lens immersed in another medium.
  1. 1

    Enough for 1 mark

    Refraction at a spherical surface describes image formation when light passes between two media separated by a curved refracting boundary. The lens maker's formula gives the focal length of a thin lens in terms of refractive index and radii of curvature of its two surfaces.

  2. 2

    Add for 2 marks

    Example: A biconvex glass lens has positive power in air because its surfaces make parallel rays converge. If placed in a medium with refractive index close to glass, its focal length increases greatly because the relative refractive index decreases.

  3. 3

    Add for 3 marks

    For a single spherical refracting surface, the object and image distances are measured from the pole of the surface and the radius is signed using the Cartesian convention.

Practice

Concept practice is coming soon

Login to access concept-level MCQs and weak-concept practice as they become available.

10 MCQs5 MinutesInstant Results
Login

Help improve this page

Found something confusing, incorrect, or missing?

Open Learning Map