Is it correct to say: Forgetting the sign convention — plugging positive u for a real object?

Real object is always in front, so u is NEGATIVE in New Cartesian convention. Assign signs BEFORE substituting.

Is it correct to say: Using mirror formula 1/v + 1/u = 1/f for a lens?

Lens formula has a MINUS sign: 1/v − 1/u = 1/f. Memorise the difference.

Is it correct to say: Confusing focal length signs: convex mirror ↔ convex lens?

Concave MIRROR: f negative. Convex LENS: f positive. Draw the table once and stick it above your desk.

Is it correct to say: Not converting focal length to metres before finding power?

P = 1/f with f STRICTLY in metres. 20 cm → 0.20 m.

Is it correct to say: Assuming the image is always inverted?

Concave mirror with object inside f ⇒ virtual, erect, enlarged image. Convex mirror always ⇒ virtual erect diminished.

Is it correct to say: Using n = c/v with v in cm/s?

Both c and v must be in the same units (m/s). Otherwise n comes out ridiculous.

📄 Formula sheet (PDF)

Light — Reflection and Refraction

Laws of reflection, spherical mirrors, refraction, lens formula and magnification — NCERT Class 10 Science Ch 9

📐 10 formulas✏️ 3 examples🎯 6 practice⚖️ 6 marks🏫 CBSE📚 Class 10✓ 2025–26 syllabus

💡

Board Exam Tips

→Ray diagram for concave mirror / convex lens is a guaranteed 3-mark question — practise all 6 object positions.
→Always use the New Cartesian Sign Convention: distances measured from the pole/optical centre, along the direction of incident light are positive.
→Focal length signs — concave mirror NEGATIVE, convex lens POSITIVE, concave lens NEGATIVE, convex mirror POSITIVE. Memorise the table cold.
→Magnification sign gives image orientation: negative m = inverted, positive m = erect.
→Refractive index numericals: n = c/v OR n₂₁ = sin i / sin r. Read the question to choose.

📊 Diagram

Ray diagram showing image formation by a concave mirror and a convex lens

📐 Formulas(10)

Laws of Reflection

∠ i = ∠ r

Mirror Formula★ Board fav

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

Symbol	Meaning
$u$	Object distance from pole (m); negative for real object
$v$	Image distance from pole (m)
$f$	Focal length (m); negative for concave, positive for convex mirror

Magnification (Mirror)★ Board fav

m = \frac{h ^{'}}{h} = - \frac{v}{u}

Focal Length and Radius of Curvature

f = \frac{R}{2}

Refractive Index

n_{21} = \frac{n _{2}}{n _{1}} = \frac{s i n i}{s i n r} = \frac{v _{1}}{v _{2}}

Symbol	Meaning
$n$	Refractive index (dimensionless)
$i, r$	Angles of incidence and refraction
$v_{1}, v_{2}$	Speed of light in the two media (m/s)

Absolute Refractive Index

n = \frac{c}{v}

Lens Formula★ Board fav

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

Magnification (Lens)

m = \frac{h ^{'}}{h} = \frac{v}{u}

Power of a Lens

P = \frac{1}{f (in metres)}

Combination of Lenses in Contact

P = P_{1} + P_{2} + \dots \frac{1}{f} = \frac{1}{f _{1}} + \frac{1}{f _{2}} + \dots

✏️ Solved Examples

1Solved Exampleeasy4 steps

An object is placed 15 cm in front of a concave mirror of focal length 10 cm. Find the position of the image.

Apply sign convention: object in front ⇒ u = −15 cm; concave ⇒ f = −10 cm

u = - 15 cm, f = - 10 cm

2Solved Exampleboard4 steps

A convex lens of focal length 20 cm forms a real image 60 cm from the lens. Find the object distance and magnification.

Sign convention: real image on the other side ⇒ v = +60 cm; convex ⇒ f = +20 cm

v = + 60 cm, f = + 20 cm

3Solved ExampleHOTS4 steps

A convex lens of focal length 25 cm and a concave lens of focal length 10 cm are placed in contact. Find the power and focal length of the combination.

Convert focal lengths to metres with sign

f_{1} = + 0.25 m, f_{2} = - 0.10 m

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Forgetting the sign convention — plugging positive u for a real object
✓Real object is always in front, so u is NEGATIVE in New Cartesian convention. Assign signs BEFORE substituting.
2
Using mirror formula 1/v + 1/u = 1/f for a lens
✓Lens formula has a MINUS sign: 1/v − 1/u = 1/f. Memorise the difference.
3
Confusing focal length signs: convex mirror ↔ convex lens
✓Concave MIRROR: f negative. Convex LENS: f positive. Draw the table once and stick it above your desk.
4
Not converting focal length to metres before finding power
✓P = 1/f with f STRICTLY in metres. 20 cm → 0.20 m.
5
Assuming the image is always inverted
✓Concave mirror with object inside f ⇒ virtual, erect, enlarged image. Convex mirror always ⇒ virtual erect diminished.
6
Using n = c/v with v in cm/s
✓Both c and v must be in the same units (m/s). Otherwise n comes out ridiculous.

🎯 Practice Yourself

🎯Practice Yourself6 questions

Q1
An object 4 cm tall is placed 20 cm in front of a concave mirror of focal length 10 cm. Find the image position, size and nature.
Q2
The refractive index of glass is 1.5. Find the speed of light in glass. (c = 3×10⁸ m/s)
Q3
A convex lens of focal length 15 cm forms an image at 30 cm. Find the object distance and magnification.
Q4
The power of a lens is −2.5 D. Find its focal length and type.
Q5
Two lenses of power +3 D and −5 D are combined. Find the focal length of the combination.
Q6
State one difference between reflection and refraction of light.

📝 Notes

Light — Reflection and Refraction

Light travels in straight lines. When it hits a boundary between two media it can either reflect back or refract through — this chapter quantifies both.

Sign convention (New Cartesian)

Pole (mirror) or optical centre (lens) is the origin.
Distances measured in the direction of incident light are positive; opposite direction negative.
Heights measured upward from the principal axis are positive.

Concave vs convex — image quick table

Element	f sign	Real object	Image type
Concave mirror	f < 0	Beyond F	Real, inverted
Convex mirror	f > 0	Anywhere	Virtual, erect, diminished
Convex lens	f > 0	Beyond F	Real, inverted
Concave lens	f < 0	Anywhere	Virtual, erect, diminished