These difficulties are common among CBSE Class 12 Physics students. Ray optics involves several related concepts, and a small mistake in the sign convention or unit conversion can change the final answer.
The good news is that most numerical problems become manageable when you understand the physical situation, draw a diagram where necessary, identify the given quantities and apply the correct formula.
In this detailed guide from Choice Better, you will learn how to solve important ray optics numericals involving spherical mirrors, thin lenses, refraction, lens power, combinations of lenses, prisms and optical instruments. Each worked example explains the formula, substitution and reasoning behind the answer.
This guide is designed to support your CBSE Class 12 board examination preparation for 2027. Always compare your preparation with the official syllabus and the instructions for your examination session.
Table of Contents
- Understanding ray optics numericals
- Cartesian sign convention
- Spherical mirror formula and solved examples
- Thin lens formula and solved examples
- Magnification of mirrors and lenses
- Power and combination of lenses
- Refraction and total internal reflection
- Lens maker's formula
- Prism numericals
- Microscope and telescope numericals
- Important formula table
- Common mistakes and their solutions
- Practice questions with answers
- Exam preparation strategy
- Frequently asked questions
1. Understanding Ray Optics Numericals
Ray optics describes the behaviour of light using rays. It is useful for studying reflection, refraction, image formation by mirrors and lenses, and the operation of optical instruments.
In numerical problems, you are usually given some physical quantities and asked to calculate another quantity. For example, you might know the object distance and focal length of a lens and need to calculate the image distance.
Before solving a problem, identify which part of ray optics it belongs to.
- Reflection: Light changes direction when it reflects from a surface. Spherical mirrors form images according to the mirror equation.
- Refraction: Light changes direction when it travels between media with different refractive indices.
- Lenses: Convex and concave lenses form images through refraction.
- Optical instruments: Microscopes and telescopes use lenses or mirrors to produce magnified images.
- Prisms: Light changes direction through refraction at two surfaces and may undergo dispersion.
For additional practice with formula selection, read our complete guide to solving CBSE Class 12 Physics numericals. It explains a systematic method that you can apply to ray optics and other Physics chapters.
2. Cartesian Sign Convention: The Foundation of Ray Optics
Before substituting values into mirror or lens equations, learn the Cartesian sign convention. It helps you distinguish between real and virtual images and prevents many avoidable calculation errors.
Under the usual Cartesian convention:
- The pole of a spherical mirror or the optical centre of a thin lens is the origin.
- Distances measured in the direction of incident light are positive.
- Distances measured opposite to the direction of incident light are negative.
- Heights above the principal axis are positive.
- Heights below the principal axis are negative.
For the usual arrangement where light travels from left to right, the object is commonly placed on the left side. Its object distance is therefore negative.
| Quantity | Usual sign | Explanation |
|---|---|---|
| Object distance u | Negative | Object lies on the incident-light side |
| Focal length of a concave mirror | Negative | Focus lies in front of the mirror |
| Focal length of a convex mirror | Positive | Focus is virtual and lies behind the mirror |
| Focal length of a convex lens | Positive | Converging lens |
| Focal length of a concave lens | Negative | Diverging lens |
| Real image formed by a mirror | Usually v negative | Image forms in front of the mirror |
| Real image formed by a lens | Usually v positive | Image forms on the side opposite the object |
These signs describe the standard arrangement and must be applied consistently. If the direction of incident light or the arrangement changes, interpret the axes and signs accordingly.
A simple rule to remember
Do not memorise signs independently of the diagram. Draw the principal axis, mark the object, identify the direction of light and then assign signs to distances.
3. Spherical Mirror Formula: Important Solved Numericals
Spherical mirrors include concave and convex mirrors. A concave mirror can produce real or virtual images depending on the object's position, whereas a convex mirror produces a virtual, erect and diminished image for a real object placed in front of it.
Mirror formula
1/f = 1/v + 1/u
Here:
- f = focal length of the mirror
- v = image distance
- u = object distance
The radius of curvature and focal length are related by:
f = R/2
This relationship applies to spherical mirrors under the paraxial approximation.
Example 1: Image formed by a concave mirror
Question: An object is placed 30 cm in front of a concave mirror of focal length 15 cm. Calculate the image distance.
Step 1: Write the given quantities.
u = -30 cm and f = -15 cm.
Step 2: Apply the mirror formula.
1/f = 1/v + 1/u
Step 3: Substitute the values.
-1/15 = 1/v - 1/30
1/v = -1/15 + 1/30
1/v = -2/30 + 1/30 = -1/30
Final answer: v = -30 cm.
The image forms 30 cm in front of the mirror. It is real and inverted. Since the object is at the centre of curvature, the image is of the same size as the object.
Example 2: Image formed by a convex mirror
Question: An object is placed 30 cm in front of a convex mirror having a focal length of 20 cm. Find the image distance.
Given: u = -30 cm and f = +20 cm.
Using the mirror formula:
1/20 = 1/v - 1/30
1/v = 1/20 + 1/30
1/v = 3/60 + 2/60 = 5/60 = 1/12
Final answer: v = +12 cm.
The positive image distance indicates that the image is behind the mirror. It is virtual, erect and diminished.
Example 3: Finding the focal length of a mirror
Question: A concave mirror forms a real image 24 cm in front of it when an object is placed 40 cm in front of it. Calculate the focal length.
Given: u = -40 cm and v = -24 cm.
Using the mirror formula:
1/f = 1/v + 1/u
1/f = -1/24 - 1/40
1/f = -5/120 - 3/120 = -8/120 = -1/15
Final answer: f = -15 cm.
The negative focal length confirms that the mirror is concave under the adopted convention.
Example 4: Finding the radius of curvature
Question: A concave mirror has a focal length of -18 cm. Calculate its radius of curvature.
Using f = R/2:
R = 2f = 2 × (-18)
Final answer: R = -36 cm.
The magnitude of the radius of curvature is 36 cm. The negative sign indicates the centre of curvature is in front of the mirror.
4. Thin Lens Formula: Important Solved Numericals
A convex lens is thicker at the centre and normally converges parallel rays of light. A concave lens is thinner at the centre and normally diverges parallel rays.
The thin lens formula using the Cartesian sign convention is:
1/f = 1/v - 1/u
Notice that this equation is different from the mirror formula. Avoid using the same equation for both situations.
Example 5: Image distance for a convex lens
Question: An object is placed 30 cm in front of a convex lens with a focal length of 15 cm. Calculate the image distance.
Given: u = -30 cm and f = +15 cm.
Using the lens formula:
1/15 = 1/v - 1/(-30)
1/15 = 1/v + 1/30
1/v = 1/15 - 1/30
1/v = 1/30
Final answer: v = +30 cm.
The image is real and inverted. The object is placed at twice the focal length, so the image is formed at twice the focal length on the other side and has the same size as the object.
Example 6: Image distance for a concave lens
Question: An object is placed 30 cm in front of a concave lens having a focal length of -20 cm. Find the image distance.
Given: u = -30 cm and f = -20 cm.
Using the lens formula:
-1/20 = 1/v - 1/(-30)
-1/20 = 1/v + 1/30
1/v = -1/20 - 1/30
1/v = -3/60 - 2/60 = -5/60 = -1/12
Final answer: v = -12 cm.
The image forms on the same side as the object. For this ordinary real-object arrangement, it is virtual, erect and diminished.
Example 7: Finding the focal length of a convex lens
Question: An object is placed 20 cm in front of a lens, and a real image forms 60 cm on the other side. Find the focal length.
Given: u = -20 cm and v = +60 cm.
Using the lens formula:
1/f = 1/v - 1/u
1/f = 1/60 - (-1/20)
1/f = 1/60 + 3/60 = 4/60 = 1/15
Final answer: f = +15 cm.
The positive focal length indicates a converging lens in air.
5. Magnification of Mirrors and Lenses
Magnification compares the height of the image with the height of the object. It tells you whether the image is enlarged or diminished and whether it is erect or inverted.
Magnification for spherical mirrors
m = hᵢ/hₒ = -v/u
Magnification for thin lenses
m = hᵢ/hₒ = v/u
Here, hᵢ is image height and hₒ is object height.
- Positive magnification usually indicates an erect image under the standard convention.
- Negative magnification indicates an inverted image.
- The magnitude |m| greater than 1 indicates an enlarged image.
- The magnitude |m| less than 1 indicates a diminished image.
- The magnitude |m| equal to 1 indicates an image of the same size.
Example 8: Finding magnification of a lens
Question: An object of height 4 cm is placed in front of a convex lens. The image forms at a distance of +30 cm, while the object distance is -15 cm. Calculate magnification and image height.
Given: v = +30 cm, u = -15 cm and hₒ = 4 cm.
m = v/u = 30/(-15) = -2.
Since m = hᵢ/hₒ:
hᵢ = m × hₒ = -2 × 4 = -8 cm.
Final answer: Magnification = -2 and image height = -8 cm.
The image is inverted and twice the height of the object.
6. Power of a Lens and Combination of Lenses
The power of a lens describes its converging or diverging ability. It is especially useful when lenses are prescribed for correcting vision or combined in an optical system.
Power formula: P = 1/f
Here, focal length f must be in metres and power P is measured in dioptres (D).
- Convex lens: positive power.
- Concave lens: negative power.
Example 9: Power of a convex lens
Question: Calculate the power of a convex lens with focal length 25 cm.
Convert the focal length:
f = +25 cm = +0.25 m.
P = 1/0.25 = +4 D.
Final answer: +4 dioptres.
Example 10: Power of a concave lens
Question: A concave lens has a focal length of -50 cm. Find its power.
f = -0.50 m.
P = 1/(-0.50) = -2 D.
Final answer: -2 dioptres.
Combination of thin lenses in contact
For thin lenses in contact in air, the equivalent power is the algebraic sum of the individual powers:
P = P₁ + P₂ + P₃ + ...
Equivalently, 1/F = 1/f₁ + 1/f₂ + 1/f₃ + ..., provided the focal lengths are expressed in consistent units.
Example 11: Two lenses in contact
Question: Two thin lenses in contact have powers +3 D and -1 D. Find their equivalent power and focal length.
P = P₁ + P₂ = 3 + (-1) = +2 D.
Focal length F = 1/P = 1/2 m.
Final answer: Equivalent power = +2 D and focal length = +0.5 m or +50 cm.
Remember to use signed powers. Adding the magnitudes without considering the signs can produce an incorrect result.
7. Refraction and Total Internal Reflection Numericals
Refraction occurs when light passes from one medium to another and its speed changes. The direction may also change, depending on the angle of incidence and the refractive indices.
Snell's law
n₁ sin i = n₂ sin r
Here, n₁ and n₂ are the refractive indices of the first and second media, while i and r are the angles of incidence and refraction measured from the normal.
Example 12: Finding the angle of refraction
Question: Light travels from air into glass of refractive index 1.5. If the angle of incidence is 30°, calculate the angle of refraction.
Taking the refractive index of air as approximately 1:
1 × sin 30° = 1.5 × sin r
0.5 = 1.5 sin r
sin r = 0.5/1.5 = 1/3.
r = sin⁻¹(1/3) ≈ 19.5°.
Final answer: The angle of refraction is approximately 19.5°.
The ray bends towards the normal because it enters a medium with a higher refractive index.
Critical angle and total internal reflection
When light travels from an optically denser medium to a less dense medium, the critical angle C is the angle of incidence for which the angle of refraction is 90°.
For two transparent media where n₁ is greater than n₂:
sin C = n₂/n₁
If the second medium is air, this becomes approximately sin C = 1/n, where n is the refractive index of the denser medium relative to air.
Example 13: Finding the critical angle
Question: Calculate the critical angle for glass of refractive index 1.5 surrounded by air.
sin C = 1/1.5 = 0.6667.
C = sin⁻¹(0.6667) ≈ 41.8°.
Final answer: The critical angle is approximately 41.8°.
Total internal reflection occurs when light travels from the denser medium towards the less dense medium and the angle of incidence exceeds the critical angle. The incident angle must be greater than C, not merely equal to it.
Applications include optical fibres, which guide light through repeated total internal reflection.
8. Lens Maker's Formula
The lens maker's formula connects the focal length of a thin lens with its refractive index and the radii of curvature of its two surfaces.
For a thin lens in air:
1/f = (n - 1)(1/R₁ - 1/R₂)
Here:
- f is the focal length of the lens.
- n is the refractive index of the lens material relative to air.
- R₁ and R₂ are the signed radii of curvature of the first and second surfaces, following the Cartesian convention.
Example 14: Finding focal length using the lens maker's formula
Question: A thin symmetric biconvex lens is made of glass with refractive index 1.5. Its first surface has radius of curvature +20 cm and its second surface has radius -20 cm. Find its focal length in air.
Given: n = 1.5, R₁ = +20 cm and R₂ = -20 cm.
1/f = (1.5 - 1)(1/20 - 1/(-20))
1/f = 0.5(1/20 + 1/20)
1/f = 0.5 × 1/10 = 1/20.
Final answer: f = +20 cm.
The positive focal length is consistent with a converging biconvex lens under these conditions.
9. Prism Numericals for CBSE Class 12
When light passes through a prism, it refracts at both surfaces. The angle of deviation depends on the prism angle and the angles of incidence and emergence.
The angle of deviation is:
δ = i + e - A
Here, i is the angle of incidence, e is the angle of emergence and A is the prism angle.
At minimum deviation, the path through the prism is symmetric:
i = e
Also, the refraction angles inside the prism are equal, and:
n = sin[(A + δₘ)/2] / sin(A/2)
Here, δₘ is the angle of minimum deviation and n is the refractive index of the prism material relative to the surrounding medium.
Example 15: Calculating deviation through a prism
Question: A ray enters a prism at an angle of incidence 45° and emerges at an angle of 40°. If the prism angle is 60°, calculate the angle of deviation.
δ = i + e - A.
δ = 45° + 40° - 60°.
Final answer: δ = 25°.
Example 16: Refractive index at minimum deviation
Question: A prism has an angle of 60° and a minimum deviation of 30°. Calculate its refractive index relative to air.
n = sin[(A + δₘ)/2] / sin(A/2)
n = sin[(60° + 30°)/2] / sin(60°/2)
n = sin 45° / sin 30°
n = (√2/2)/(1/2) = √2.
Final answer: n ≈ 1.414.
10. Microscope and Telescope Numericals
Optical instruments use lenses or mirrors to produce magnified or otherwise useful images. For numerical problems, read the question carefully to determine whether it asks for linear magnification, angular magnifying power or the length of an instrument.
10.1 Compound microscope
A compound microscope uses an objective lens and an eyepiece. The objective produces an enlarged intermediate image, which the eyepiece magnifies further.
For a compound microscope, the total magnifying power is the product of the magnifications of the objective and eyepiece, using the appropriate definitions and sign conventions.
For a microscope adjusted for a final image at infinity, the magnitude of angular magnifying power is approximately:
|M| ≈ (L/fₒ)(D/fₑ)
Here, L is the tube length under the usual approximation, fₒ is the objective focal length, fₑ is the eyepiece focal length and D is the least distance of distinct vision, conventionally taken as 25 cm in standard textbook problems.
Example 17: Magnifying power of a compound microscope
Question: A compound microscope has a tube length of 16 cm. The focal length of the objective is 0.8 cm, and the eyepiece focal length is 4 cm. Estimate its magnifying power for a final image at infinity, using D = 25 cm.
|M| ≈ (L/fₒ)(D/fₑ)
|M| ≈ (16/0.8)(25/4)
|M| ≈ 20 × 6.25.
Final answer: The approximate magnifying power is 125.
This is a standard approximate result; detailed instrument problems may require more precise image-position relationships or a different final-image condition.
10.2 Astronomical telescope
An astronomical telescope is used to view distant objects. In normal adjustment, the final image is at infinity and the angular magnifying power in magnitude is:
|M| = fₒ/fₑ
The approximate distance between the objective and eyepiece in normal adjustment is:
L = fₒ + fₑ
Here, fₒ is the objective focal length and fₑ is the eyepiece focal length.
Example 18: Magnifying power of a telescope
Question: An astronomical telescope has an objective focal length of 100 cm and an eyepiece focal length of 5 cm. Find its magnifying power in normal adjustment.
|M| = fₒ/fₑ = 100/5.
Final answer: The magnitude of angular magnifying power is 20.
The final image is inverted relative to the distant object in the usual astronomical telescope arrangement. The formula above gives the magnitude, not the orientation sign.
Example 19: Length of an astronomical telescope
Question: An astronomical telescope has an objective focal length of 80 cm and an eyepiece focal length of 4 cm. Calculate its length in normal adjustment.
L = fₒ + fₑ = 80 + 4.
Final answer: L = 84 cm.
11. Important Ray Optics Formula Table
Use this table as a quick revision sheet. Check the sign convention and conditions before applying each equation.
| Concept | Formula |
|---|---|
| Spherical mirror | 1/f = 1/v + 1/u |
| Mirror radius | f = R/2 |
| Thin lens | 1/f = 1/v - 1/u |
| Mirror magnification | m = -v/u |
| Lens magnification | m = v/u |
| Lens power | P = 1/f, with f in metres |
| Thin lenses in contact | P = P₁ + P₂ + ... |
| Snell's law | n₁ sin i = n₂ sin r |
| Critical angle | sin C = n₂/n₁, for n₁ greater than n₂ |
| Lens maker's formula in air | 1/f = (n - 1)(1/R₁ - 1/R₂) |
| Prism deviation | δ = i + e - A |
| Prism at minimum deviation | n = sin[(A + δₘ)/2] / sin(A/2) |
| Telescope in normal adjustment | |M| = fₒ/fₑ |
| Telescope length in normal adjustment | L = fₒ + fₑ |
12. Common Mistakes in Ray Optics Numericals
Mistake 1: Using the mirror formula for a lens
The mirror formula is 1/f = 1/v + 1/u, while the thin lens formula is 1/f = 1/v - 1/u under the Cartesian sign convention. Write the correct equation before substituting values.
Mistake 2: Ignoring negative signs
A concave mirror normally has negative focal length under the standard convention, while a convex lens has positive focal length. A sign error can lead to a wrong image position or an incorrect conclusion about the image.
Mistake 3: Using centimetres in the lens power formula
The formula P = 1/f gives power in dioptres only when f is expressed in metres. Convert 20 cm to 0.20 m before calculating power.
Mistake 4: Confusing the angle with its complement
For Snell's law and critical-angle calculations, angles are measured from the normal. Do not use the angle measured from the surface unless you first convert it.
Mistake 5: Forgetting what magnification means
A negative magnification indicates an inverted image under the usual convention. A positive magnification indicates an erect image. The magnitude tells you whether the image is enlarged or diminished.
Mistake 6: Memorising an optical instrument formula without its conditions
The magnifying power of a microscope or telescope depends on the final-image condition. Check whether the question specifies normal adjustment, a final image at infinity or a final image at the least distance of distinct vision.
Mistake 7: Skipping diagrams when the arrangement is unclear
A quick ray diagram can help you understand whether the image should be real or virtual. Even when a diagram is not explicitly required, sketching one during rough work can prevent errors.
For a broader strategy to improve calculation accuracy, see our step-by-step Physics numericals guide for CBSE Class 12.
13. Practice Questions: Test Your Ray Optics Skills
Try each question without checking the answer first. Write the formula, substitute the values and include the final unit where applicable.
Question 1: Concave mirror
An object is placed 20 cm in front of a concave mirror with focal length 10 cm. Find the image distance.
Show answer
u = -20 cm, f = -10 cm.
1/v = 1/f - 1/u = -1/10 + 1/20 = -1/20.
Answer: v = -20 cm. The image is real and inverted.
Question 2: Convex lens
An object is placed 24 cm in front of a convex lens of focal length 12 cm. Find the image distance.
Show answer
u = -24 cm, f = +12 cm.
1/v = 1/f + 1/u = 1/12 - 1/24 = 1/24.
Answer: v = +24 cm.
Question 3: Lens power
Find the power of a concave lens with focal length -0.20 m.
Show answer
P = 1/f = 1/(-0.20).
Answer: -5 D.
Question 4: Lens magnification
An object of height 3 cm forms an image at +18 cm when the object is at -12 cm from a thin lens. Find the magnification and image height.
Show answer
m = v/u = 18/(-12) = -1.5.
hᵢ = m × hₒ = -1.5 × 3 = -4.5 cm.
Answer: m = -1.5 and hᵢ = -4.5 cm.
Question 5: Refraction
Light travels from air into glass of refractive index 1.5 at an incidence angle of 45°. Calculate the angle of refraction.
Show answer
sin r = sin 45°/1.5 = 0.7071/1.5 ≈ 0.4714.
r = sin⁻¹(0.4714) ≈ 28.1°.
Answer: Approximately 28.1°.
Question 6: Critical angle
Calculate the critical angle for a material of refractive index 1.6 relative to air.
Show answer
sin C = 1/1.6 = 0.625.
C = sin⁻¹(0.625) ≈ 38.7°.
Answer: Approximately 38.7°.
Question 7: Two lenses in contact
Two thin lenses in contact have powers +5 D and -2 D. Find the equivalent focal length.
Show answer
P = +5 - 2 = +3 D.
F = 1/3 m ≈ 0.333 m.
Answer: Approximately +33.3 cm.
Question 8: Prism deviation
A prism has an angle of 50°. A ray enters at 40° and emerges at 35°. Calculate the angle of deviation.
Show answer
δ = i + e - A = 40° + 35° - 50°.
Answer: 25°.
Question 9: Astronomical telescope
A telescope has an objective focal length of 120 cm and an eyepiece focal length of 6 cm. Find its magnifying power in normal adjustment.
Show answer
|M| = fₒ/fₑ = 120/6.
Answer: 20.
Question 10: Lens maker's formula
A thin symmetric biconvex lens has refractive index 1.5 and surface radii +30 cm and -30 cm. Find its focal length in air.
Show answer
1/f = (1.5 - 1)(1/30 - 1/(-30)) = 0.5 × 2/30 = 1/30.
Answer: +30 cm.
14. How to Prepare Ray Optics for the CBSE Board Examination
Learning formulas is only one part of preparation. You should also practise selecting equations, interpreting diagrams and presenting your working clearly.
Step 1: Revise one concept at a time
Start with spherical mirrors, then move to lenses, refraction, lens power, prisms and optical instruments. Practise a few direct questions before combining concepts.
Step 2: Maintain a formula notebook
Record each formula with the meaning of its symbols, sign conventions and conditions of use. Include one short solved example beside formulas you frequently confuse.
Step 3: Practise without looking at solutions
After studying a worked example, close the notes and solve it again. Then attempt a similar problem with different numerical values. This reveals whether you understand the method or have only memorised the answer.
Step 4: Review your mistakes
Record whether each error came from formula selection, signs, units, arithmetic or interpretation of the question. Reattempt incorrect problems after a short gap.
Step 5: Use official examination resources
Check the official CBSE 2026–27 curriculum to verify prescribed content and use the CBSE Class XII sample papers and marking schemes for examination practice.
For a complete revision routine across subjects, follow the Choice Better CBSE Class 12 study plan for the 2027 board exams. Use it to allocate time for Physics while maintaining progress in Chemistry and Biology or Mathematics.
Step 6: Improve answer presentation
For each numerical, write the relevant formula, substitute signed values, show the calculation and state the final result clearly. Add a labelled diagram when it helps explain the situation or is required by the question.
For general learning and retention, you can also use our guide to effective revision techniques for exams.
15. Frequently Asked Questions About Ray Optics Numericals
Q1. Which formulas are important in Class 12 Ray Optics?
Important relationships include the mirror formula, thin lens formula, magnification, power of a lens, lens maker's formula, Snell's law, the critical-angle relationship, prism deviation and the magnifying power of optical instruments. Verify the current syllabus before finalising your revision list.
Q2. What is the difference between the mirror formula and lens formula?
Using the Cartesian sign convention, the mirror formula is 1/f = 1/v + 1/u, whereas the thin lens formula is 1/f = 1/v - 1/u. Identify the optical system before choosing the equation.
Q3. Why is the focal length of a concave mirror negative?
Under the standard Cartesian convention, a concave mirror's principal focus lies in front of the mirror, opposite to the positive direction of the incident light axis. Its focal length is therefore negative.
Q4. Why must focal length be converted into metres when calculating lens power?
Power in dioptres is defined as the reciprocal of focal length in metres. If focal length is given in centimetres, convert it to metres first to obtain the correct numerical value in dioptres.
Q5. What does negative magnification mean?
Negative magnification indicates an inverted image under the usual sign convention. The magnitude of magnification indicates whether the image is larger or smaller than the object.
Q6. When does total internal reflection occur?
Light must travel from an optically denser medium to an optically less dense medium, and the angle of incidence must exceed the critical angle. Both conditions are necessary.
Q7. What is the power of two lenses in contact?
For thin lenses in contact in air, their equivalent power is the algebraic sum of their individual powers: P = P₁ + P₂. Use the correct positive or negative sign for each lens.
Q8. How can I get better at ray optics numericals?
Practise the sign convention first, then solve mirror and lens problems before moving to refraction, prisms and optical instruments. Check units, draw diagrams when needed and review every incorrect answer.
Q9. Are optical instruments included in the CBSE Class 12 Physics syllabus for 2026–27?
The official CBSE Physics curriculum for 2026–27 lists microscopes and astronomical telescopes, including their magnifying powers, under Ray Optics and Optical Instruments. Check the official curriculum for the complete prescribed scope.
Q10. Should I practise only previous-year questions?
No. Use NCERT material, relevant worked examples, practice problems and official sample papers together. This gives you a stronger understanding of concepts and helps you apply formulas to different question formats.
Conclusion: Build Confidence One Numerical at a Time
Ray optics becomes much more manageable when you understand the sign convention and know why each formula applies. Begin with direct mirror and lens problems, practise magnification and lens power, and then progress to refraction, prisms and optical instruments.
Do not rush through solutions simply to complete more questions. Write each step clearly, check your signs and units, and learn from mistakes. Regular practice will help you recognise familiar patterns and approach unfamiliar problems more confidently.
Your action plan for today: revise the mirror and lens formulas, solve five numerical problems without looking at the answers, and record any mistakes in a separate notebook. Reattempt the incorrect questions the next day.
Combine this focused practice with your overall Class 12 timetable and other subject-specific guides on Choice Better. A steady routine is more effective than last-minute formula memorisation.
About the Author
Sadashiba Sahu | Choice Better Blog
Choice Better publishes practical educational resources on study strategies, examination preparation, productivity and career guidance. The aim is to help students understand concepts, organise their learning and prepare more effectively through clear explanations and structured practice.
For examination preparation, readers should cross-check prescribed topics and assessment requirements against the latest official CBSE curriculum and examination resources.
