What are the formulas for Mirror Formula and Lens Formula?

- **Mirror Formula:** \frac{1}{f} = \frac{1}{v} + \frac{1}{u}, Magnification m = -\frac{v}{u} = \frac{h_i}{h_o} - **Lens Formula:** \frac{1}{f} = \frac{1}{v} - \frac{1}{u}, Magnification m = +\frac{v}{u} = \frac{h_i}{h_o}

Why are convex mirrors used as rear-view (wing) mirrors in automobiles?

1. A convex mirror always produces an **erect, virtual, and diminished** image of objects behind the vehicle. 2. Because its reflective surface curves outwards, it provides a much **wider field of view** than a plane or concave mirror, enabling the driver to view a large traffic area.

What does Snell's Law of Refraction state and what is refractive index?

Snell's Law states: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for light of a given colour and given pair of media: \frac{\sin i}{\sin r} = n_{21} = \frac{n_2}{n_1} = \frac{v_1}{v_2}. Refractive index of a medium with respect to vacuum is absolute refractive index n = \frac{c}{v}.

What is the definition and SI unit of the Power of a Lens ($P$)?

Power of a lens is the degree of convergence or divergence of light rays achieved by it, defined as the reciprocal of its focal length in metres: P = \frac{1}{f\text{ (in metres)}}. The SI unit is **Dioptre (D)** (1\text{ D} = 1\text{ m}^{-1}). A convex lens has positive power (+D); a concave lens has negative power (-D).

Where should an object be placed in front of a concave mirror to obtain a virtual and erect image?

The object must be placed **between the Pole (P) and the Principal Focus (F)** of the concave mirror. The resulting image is formed behind the mirror, enlarged (magnified, m > 1), virtual, and erect. This position is used in dentist mirrors and shaving mirrors.

What is the lateral displacement produced when light passes through a rectangular glass slab?

When a light ray enters a rectangular glass slab, it bends towards the normal at the first air-glass interface and bends away from the normal by an equal amount at the second glass-air interface. The emergent ray is **parallel** to the incident ray but shifted sideways by a perpendicular distance called **lateral displacement**.

All Revision Notes

ScienceCh-9 15 min comprehensive revision

NCERT Class 10 Science — Chapter 10

Light – Reflection and Refraction

Laws of reflection and refraction, Snell's law, spherical mirrors (concave/convex), Mirror formula & magnification, thin spherical lenses (convex/concave), Lens formula & power ( $P = 1/f$ ), and ray diagrams.

Quick Key Takeaways:

Cartesian Sign Convention: Pole/Optical centre is origin. Object distance

u

is always negative (

-u

). Focal length

f

is negative for Concave (mirror/lens) and positive for Convex (mirror/lens).

Mirror Formula & Magnification:

\frac{1}{v} + \frac{1}{u} = \frac{1}{f}, \quad m = -\frac{v}{u} = \frac{h_i}{h_o}

(

m < 0 \implies

Real & Inverted;

m > 0 \implies

Virtual & Erect).

Lens Formula & Magnification:

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}, \quad m = +\frac{v}{u} = \frac{h_i}{h_o}

Snell's Law & Refractive Index:

\frac{\sin i}{\sin r} = n_{21} = \frac{n_2}{n_1} = \frac{v_1}{v_2}, \quad n = \frac{c}{v}

Power of a Lens:

P = \frac{1}{f\text{ (in meters)}} \text{ (in Dioptres, D)}

(

P > 0

for Convex lens,

P < 0

for Concave lens).

Optics CalculatorCalculate lens/mirror distances, magnification, and lens power

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Jump to Concept:1. 1. Reflection, Spherical Mirrors & Ray Tracing Conventions 2. 2. Refraction, Snell's Law, Thin Lens Formula & Optical Power 3. 3. High-Yield Solved Board Examination Questions (3-Mark & 5-Mark)4. 4. Practical Laboratory & Competency-Based Case Drill: Tracing the Path of Light Ray through Glass Slab (NCERT Activity 10.10)5. 5. CBSE Examiner Marking Scheme, Scientific Notation & Deduction Traps

1. Reflection, Spherical Mirrors & Ray Tracing Conventions

Fundamental Principles

Core scientific laws, chemical equations, anatomical structures, and visual model for Light – Reflection and Refraction.

• Spherical Mirror Ray Tracing & Image Formation Rules

•

Concave Mirror (Converging):
- Ray parallel to principal axis passes through Principal Focus (

F

) after reflection.
- Ray through Focus becomes parallel to principal axis.
- Ray through Centre of Curvature (

C

) reflects back along the same path (

i=0^\circ

).
- Special Case: When object is between

P

and

F

\implies

Virtual, Erect, and Magnified image formed behind the mirror (used as shaving mirror and dentist mirror).

•

Convex Mirror (Diverging):
- Always forms a Virtual, Erect, and Diminished image behind the mirror between

P

and

F

regardless of object position.
- Used as Rear-View Mirror in vehicles because it gives an erect image and a much wider field of view.

📊 Light: Ray Optics, Sign Conventions & Lens PowerVisual Model

Visual schematic mapping spherical mirror and lens ray tracing rules, Cartesian sign conventions, lateral displacement in glass slabs, and dioptre power.

2. Refraction, Snell's Law, Thin Lens Formula & Optical Power

Mechanisms & Experiments

Step-by-step chemical reaction mechanisms, experimental activities, and physiological pathways for Light – Reflection and Refraction.

• Laws of Refraction & Lens Physics

•

Snell's Law: The ratio of the sine of angle of incidence to the sine of angle of refraction is constant for a given pair of media:

\frac{\sin i}{\sin r} = n_{21}

•

Refraction through Rectangular Glass Slab:
- Emergent ray is parallel to incident ray but laterally displaced.
- Lateral displacement increases with slab thickness, refractive index, and angle of incidence.

•

Convex Lens (Converging) vs Concave Lens (Diverging):
- Convex lens forms real inverted images for

u > f

; forms virtual magnified erect image for

u < f

(used as magnifying glass).
- Concave lens always forms virtual, erect, and diminished images on the same side as the object.

3. High-Yield Solved Board Examination Questions (3-Mark & 5-Mark)

Solved Board Questions

Standard CBSE board exam questions with complete scientific justifications and marking scheme step protocols.

• 3-Mark Standard Board Question: A convex mirror used for rear-view on an automobile has a radius of curvature of 3.00 m. If a bus is located at 5.00 m from this mirror, find the position, nature and size of the image.

•

Step 1 (Given Data with Sign Convention):
- Radius of curvature

R = +3.00

\implies

Focal length

f = +\frac{R}{2} = +1.50

m.
- Object distance

u = -5.00

m.
- Image distance

v = ?

, Magnification

m = ?

•

Step 2 (Applying Mirror Formula):

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

\frac{1}{v} = \frac{1}{1.50} - \left(-\frac{1}{5.00}\right) = \frac{1}{1.50} + \frac{1}{5.00} = \frac{10}{15} + \frac{1}{5} = \frac{2}{3} + \frac{1}{5} = \frac{10 + 3}{15} = \frac{13}{15}

\mathbf{v = +\frac{15}{13}\text{ m} = +1.15\text{ meters}}

•

Step 3 (Magnification & Nature):

m = -\frac{v}{u} = -\frac{+1.15}{-5.00} = \mathbf{+0.23}

•

Conclusion: The image is formed at a distance of $1.15$ m behind the mirror. The positive sign of

m

and

v

indicates that the image is Virtual, Erect, and Diminished (reduced to 0.23 times the size of the bus).

• 5-Mark Comprehensive Question / Numerical: A 2.0 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 10 cm. The distance of the object from the lens is 15 cm. Find the nature, position and size of the image. Also find its magnification and power of the lens.

•

Step 1 (Given Data):

h_o = +2.0

cm,

f = +10

cm (convex lens),

u = -15

cm.

•

Step 2 (Applying Lens Formula):

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

\frac{1}{v} = \frac{1}{10} + \left(\frac{1}{-15}\right) = \frac{1}{10} - \frac{1}{15} = \frac{3 - 2}{30} = \frac{1}{30}

\mathbf{v = +30\text{ cm}}

•

Step 3 (Magnification and Image Height):

m = \frac{v}{u} = \frac{+30}{-15} = \mathbf{-2}

m = \frac{h_i}{h_o} \implies h_i = m \times h_o = -2 \times 2.0 = \mathbf{-4.0\text{ cm}}

•

Step 4 (Power of Lens):

f = 10\text{ cm} = 0.1\text{ m} \implies P = \frac{1}{f} = \frac{1}{0.1} = \mathbf{+10\text{ D}}

•

Final Boxed Summary:

\mathbf{\text{Image Position } v = +30\text{ cm (on other side), Nature: Real and Inverted, Size } h_i = 4.0\text{ cm (magnified), Power } = +10\text{ D}}

4. Practical Laboratory & Competency-Based Case Drill: Tracing the Path of Light Ray through Glass Slab (NCERT Activity 10.10)

Practical & Case Drill

Experimental observation analysis, chemical gas tests, and assertion-reason drills.

• Laboratory Activity Context: Tracing the Path of Light Ray through Glass Slab (NCERT Activity 10.10)

A ray of light enters from air into a rectangular glass slab at an angle of incidence $i = 45^\circ$ and emerges into air at angle $e$ .

•

Q1: What is the relationship between the angle of incidence ( $i$ ) and angle of emergence ( $e$ )?

\rightarrow

The angle of incidence equals the angle of emergence:

\mathbf{\angle i = \angle e}

(since opposite faces of the slab are parallel).

•

Q2: Does the emergent ray deviate in direction?

\rightarrow

No, the emergent ray is parallel to the incident ray; it only undergoes a sideways shift called lateral displacement.

•

Q3: State two factors on which lateral displacement depends.

\rightarrow

(1) Thickness of the glass slab (greater thickness

\implies

larger displacement); (2) Refractive index of the glass material.

5. CBSE Examiner Marking Scheme, Scientific Notation & Deduction Traps

Important Solved Board Questions

Examiner step-marking allocations, mandatory scientific terminology, and common error avoidance.

• Step-by-Step Marking Rubric & Key Terminology

•

1 Mark: Applying Cartesian sign convention accurately (

u

negative, correct sign for

f

•

2 Marks: Step-by-step substitution and algebraic solution of mirror/lens formula.

•

1 Mark: Correct magnification formula (

m = -v/u

for mirror;

m = +v/u

for lens).

•

1 Mark: Calculating power in Dioptres with focal length converted to meters.

• Common Error Deduction Traps

•

Trap 1: Forgetting that focal length must be in meters when calculating lens power

P = 1/f

(

f = 20

\implies f = 0.2

\implies P = +5

D).

•

Trap 2: Confusing the sign in mirror formula (

+1/u

) with lens formula (

-1/u

•

Trap 3: Forgetting arrows on rays in ray diagrams (CBSE examiners deduct 0.5 marks per ray without arrows).

Authentic Board Question (5 Marks)Topic: Spherical Mirrors & Mirror Formula

A concave mirror produces a real inverted image of magnification

-2

when an object is placed at a distance of

30\text{ cm}

in front of it. (a) Find the position of the image. (b) Calculate the focal length of the mirror. (c) Draw a neat ray diagram to show image formation.

Official CBSE Step-by-Step Marking Breakdown:

Part (a): Image Position ($v$):

m = -\frac{v}{u} \implies -2 = -\frac{v}{-30} \implies v = -60\text{ cm}

(in front of mirror).

1½ Marks

Part (b): Focal Length ($f$):

\frac{1}{f} = \frac{1}{v} + \frac{1}{u} = \frac{1}{-60} + \frac{1}{-30} = \frac{-3}{60} \implies f = -20\text{ cm}

1½ Marks

Part (c): Ray Diagram: Accurate ray diagram with arrows showing object between

C

and

F

, and image beyond

C

2 Marks

Model Student Answer (Target: Full 5/5 Marks):

Given:
- Object distance

u = -30\text{ cm}

- Magnification

m = -2

(negative for real and inverted image)

(a) Image Position ( $v$ ):

m = -\frac{v}{u} \implies -2 = -\frac{v}{-30} \implies v = -60\text{ cm}

Answer: Image is formed at a distance of $60\text{ cm}$ in front of the mirror (on the same side as object).

(b) Focal Length ( $f$ ):
Using Mirror Formula

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

\frac{1}{f} = \frac{1}{-60} + \frac{1}{-30} = \frac{-1 - 2}{60} = \frac{-3}{60} = -\frac{1}{20}

f = -20\text{ cm}

Answer: The focal length of the concave mirror is $20\text{ cm}$ .

(c) Nature & Verification:
Since

f = 20\text{ cm}

and

R = 40\text{ cm}

, the object at

u = 30\text{ cm}

lies between Focus ( $F$ ) and Centre of Curvature ( $C$ ). The image is formed beyond $C$ , enlarged, real, and inverted.

Examiner Mark Deduction Traps:

•Applying the Cartesian sign convention to

u, v, f

is mandatory. Missing negative signs costs 1 full mark.

•Always draw directional arrows on light rays in the ray diagram.

High-Frequency Conceptual Doubts & FAQs

Curated answers to the most common questions asked by Class 10 students.

1. Object is always placed to the left of mirror/lens (object distance

u

is always negative).
2. All distances measured to the right of origin (along

+x

) are positive; to the left (along

-x

) are negative.
3. Distances measured upward perpendicular to principal axis (

+y

) are positive (erect image); downward (

-y

) are negative (inverted image).
- Focal Length ( $f$ ): Concave mirror/lens = negative; Convex mirror/lens = positive.

Light – Reflection and Refraction

1. Reflection, Spherical Mirrors & Ray Tracing Conventions

2. Refraction, Snell's Law, Thin Lens Formula & Optical Power

3. High-Yield Solved Board Examination Questions (3-Mark & 5-Mark)

4. Practical Laboratory & Competency-Based Case Drill: Tracing the Path of Light Ray through Glass Slab (NCERT Activity 10.10)

5. CBSE Examiner Marking Scheme, Scientific Notation & Deduction Traps

Official CBSE Step-by-Step Marking Breakdown:

High-Frequency Conceptual Doubts & FAQs

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