Class 12 Physics Chapter 9: Ray Optics and Optical Instruments

CBSE 2026–27 | NCERT-aligned free notes, diagrams, examples and practice

Ray optics studies reflection and refraction using the ray model of light. The chapter develops spherical mirrors, refraction, total internal reflection, lenses, optical instruments and image formation.

1. Reflection

The angle of incidence equals the angle of reflection, measured from the normal. For spherical mirrors, the mirror formula is 1/f = 1/v + 1/u and magnification m = −v/u under the Cartesian sign convention.

2. Refraction

Snell’s law: n₁ sin i = n₂ sin r. Refractive index n = c/v for a medium relative to vacuum.

3. Total Internal Reflection

When light travels from a denser to a rarer medium and the incidence angle exceeds the critical angle, total internal reflection can occur. For a medium-air boundary, sin C = 1/n.

4. Lenses

For a thin lens, 1/f = 1/v − 1/u and magnification m = v/u under the standard Cartesian convention. Lens power P = 1/f in metres, measured in dioptres.

5. Lens Combination

For thin lenses in contact, equivalent power is P = P₁ + P₂. For separated lenses, image formation must be handled sequentially or with the appropriate combination relation.

6. Optical Instruments

The human eye forms a real, inverted image on the retina. A simple microscope uses a convex lens to obtain angular magnification. Astronomical telescopes use objective and eyepiece systems to view distant objects with greater angular size.

7. Prism and Dispersion

A prism deviates light because refraction occurs at two non-parallel surfaces. White light can be dispersed into constituent colours because refractive index depends on wavelength.

Worked Example

A convex lens has focal length 20 cm and an object is placed 30 cm in front of it. Using the Cartesian sign convention, u = −30 cm and f = +20 cm. From 1/f = 1/v − 1/u, v = 60 cm. Magnification m = v/u = −2, so the image is inverted and magnified.

Common Exam Traps

• Always state the sign convention before substituting values.
• Lens and mirror formula signs differ in the standard Cartesian convention.
• Total internal reflection requires travel from optically denser to rarer medium and incidence angle above critical.
• Power uses focal length in metres.

Practice Questions

1. Derive the mirror formula or explain its terms.
2. Apply Snell’s law to a glass-air interface.
3. Explain total internal reflection and one practical application.
4. Solve a lens numerical using the Cartesian sign convention.
5. Explain the working of a simple microscope and astronomical telescope.

📌 Ray Diagram: Convex Lens Image Formation

Decision Guide for Numericals

1. Write the sign convention.
2. Identify f and u.
3. Choose the mirror or lens formula.
4. Calculate v.
5. Interpret the sign of v and magnification.
6. State whether the image is real/virtual, erect/inverted and magnified/diminished.

Application Questions

1. Why does a convex lens converge parallel rays?
2. Explain why total internal reflection is used in optical fibres.
3. An object is placed between F and 2F of a convex lens. Predict the image before calculating.
4. Why does a prism disperse white light?

Ray Diagrams & Numerical Applications

Convex Lens

Use the Cartesian sign convention consistently. Lens formula: 1/f=1/v−1/u and magnification m=v/u.

Worked Numerical

For a convex lens with f=20 cm and object distance u=−30 cm, 1/v=1/f+1/u=1/20−1/30=1/60, so v=60 cm. The image is real and inverted.

Optical Instruments

Understand the working principles and angular magnification of the microscope and astronomical telescope under the prescribed conditions.

Total Internal Reflection

Total internal reflection occurs when light travels from an optically denser medium to a rarer medium with incidence angle greater than the critical angle. It is the principle behind optical fibres.

Practice

1. Draw standard ray diagrams for mirrors and lenses.
2. Use the lens/mirror formula to locate images.
3. Calculate magnification.
4. Apply critical-angle conditions.
5. Solve optical-instrument numericals.

Common Mistakes to Avoid

• Mixing Cartesian sign conventions.
• Drawing a ray diagram without checking the object position.
• Confusing critical angle with angle of refraction.