Teach me "Lens" for state pcs exam
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Lens optics Physics state PCS exam notes convex concave ray diagrams power formula
Here is a complete, exam-focused notes on Lens (Optics) for State PCS:
LENS - Complete Notes for State PCS Exam
1. What is a Lens?
A lens is a transparent refracting medium bounded by two curved surfaces (or one curved and one plane surface). It works on the principle of refraction of light.
2. Types of Lenses
| Type | Also Called | Shape | Action on Light |
|---|---|---|---|
| Convex Lens | Converging Lens | Thicker at centre, thinner at edges | Converges (brings together) parallel rays |
| Concave Lens | Diverging Lens | Thinner at centre, thicker at edges | Diverges (spreads) parallel rays |
Memory Trick: Convex = Converging (both start with 'C' and 'onverge'), Concave = Diverging.
3. Key Terms
| Term | Definition |
|---|---|
| Optical Centre (O) | The central point of the lens. A ray passing through it goes undeviated. |
| Principal Axis | The straight line passing through both centres of curvature of the lens. |
| Principal Focus (F) | Point where parallel rays, after refraction, actually meet (convex) or appear to diverge from (concave). |
| Focal Length (f) | Distance between the optical centre and the principal focus. |
| Centre of Curvature (C) | Centre of the sphere of which each lens surface forms a part. For a lens, there are two - C1 and C2. |
| Radius of Curvature (R) | Radius of the sphere of which the lens surface is a part. R = 2f |
Sign convention for focal length:
- Convex lens: f is positive (+)
- Concave lens: f is negative (-)
4. Lens Formula
$$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$
Where:
- v = image distance (from optical centre)
- u = object distance (from optical centre)
- f = focal length
Cartesian Sign Convention:
- Distances measured in the direction of incident light = positive
- Distances opposite to incident light = negative
- Object is always placed on the left, so u is always negative
5. Magnification
$$m = \frac{v}{u} = \frac{\text{Height of image}}{\text{Height of object}}$$
| m value | Nature of Image |
|---|---|
| m > 0 (positive) | Virtual and erect |
| m < 0 (negative) | Real and inverted |
| m | |
| m | |
| m |
6. Image Formation by Convex Lens
| Position of Object | Position of Image | Nature of Image | Size |
|---|---|---|---|
| At infinity | At F (focus) | Real, Inverted | Highly diminished (point) |
| Beyond 2F | Between F and 2F | Real, Inverted | Diminished |
| At 2F | At 2F | Real, Inverted | Same size |
| Between F and 2F | Beyond 2F | Real, Inverted | Magnified |
| At F | At infinity | Real, Inverted | Highly magnified |
| Between F and O | On same side as object | Virtual, Erect | Magnified |
Key: The last position (between F and O) is how a magnifying glass works - it gives a virtual, erect, magnified image.
7. Image Formation by Concave Lens
| Position of Object | Position of Image | Nature | Size |
|---|---|---|---|
| At infinity | At focus (F), on same side as object | Virtual, Erect | Highly diminished |
| Anywhere between infinity and O | Between F and O, on same side as object | Virtual, Erect | Diminished |
Key point: A concave lens always forms a virtual, erect, and diminished image - regardless of where the object is placed.
8. Power of a Lens ⭐ (High PCS Weightage)
$$P = \frac{1}{f \text{ (in metres)}}$$
- SI Unit: Dioptre (D) - 1 D = 1 m⁻¹
- Convex lens: P is positive
- Concave lens: P is negative
Examples:
- f = +50 cm = +0.5 m → P = +2 D (convex)
- f = -25 cm = -0.25 m → P = -4 D (concave)
Combined Power of lenses in contact:
$$P_{total} = P_1 + P_2 + P_3 + \ldots$$
Combined focal length:
$$\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2}$$
9. Lens Maker's Formula
$$\frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$$
Where:
- μ (mu) = refractive index of the lens material
- R1, R2 = radii of curvature of the two surfaces
This formula explains why a lens of the same shape but made of denser glass has a shorter focal length (more power).
10. Refraction at Spherical Surfaces - Key Relationships
- For a thin lens: R = 2f
- Refractive index of glass: ~1.5
- Power in dioptre: If f is given in cm, P = 100/f(cm)
11. Applications of Lenses (Important for PCS)
| Application | Lens Used | Reason |
|---|---|---|
| Magnifying Glass | Convex | Virtual, erect, magnified image |
| Camera | Convex | Real, inverted image on film |
| Projector / Cinema | Convex | Real, inverted, magnified image on screen |
| Microscope | Two convex lenses (objective + eyepiece) | High magnification |
| Telescope | Convex objective + concave/convex eyepiece | Distant objects |
| Spectacles for myopia (short sight) | Concave | Diverges light, moves image back to retina |
| Spectacles for hyperopia (long sight) | Convex | Converges light, moves image forward to retina |
| Reading glasses | Convex | Helps focus nearby objects |
12. Common Defects of Vision & Correction ⭐
| Defect | Problem | Correction |
|---|---|---|
| Myopia (Nearsightedness) | Can see near, not far; image forms in front of retina | Concave lens |
| Hypermetropia (Farsightedness) | Can see far, not near; image forms behind retina | Convex lens |
| Presbyopia | Loss of accommodation with age | Bifocal lens (convex + concave) |
| Astigmatism | Uneven curvature of cornea/lens | Cylindrical lens |
13. Quick Formula Summary (Revision Sheet)
| Formula | What it gives |
|---|---|
| 1/v - 1/u = 1/f | Lens formula |
| m = v/u | Linear magnification |
| P = 1/f(m) | Power of lens |
| P_total = P1 + P2 | Combined power |
| 1/f = 1/f1 + 1/f2 | Combined focal length |
| P = 100/f(cm) | Quick power calculation |
14. PCS MCQ Practice Questions
Q1. A convex lens has focal length 20 cm. Its power is:
→ P = 100/20 = +5 D
Q2. Two lenses of power +3 D and -1 D are in contact. Net power:
→ P = 3 + (-1) = +2 D, f = 1/2 = 0.5 m = 50 cm
Q3. A person uses a -2 D lens. They suffer from:
→ Negative power = concave lens = Myopia
Q4. Which lens always gives a virtual image?
→ Concave lens (always virtual, erect, diminished)
Q5. Where should an object be placed before a convex lens to get same-size image?
→ At 2F (centre of curvature)
15. Key One-liners for Last-Minute Revision
- Convex = converging = positive focal length = positive power
- Concave = diverging = negative focal length = negative power
- Power unit = Dioptre (D)
- Opticians write lens power in dioptres on prescriptions (e.g., -1.5 D)
- Magnifying glass uses convex lens between F and O
- Myopia corrected by concave; Hypermetropia by convex
- A lens in water has less power than in air (lower relative refractive index)
- Combined lenses in contact: powers ADD algebraically
This covers everything tested in State PCS exams on Lenses. Focus especially on Power of Lens, image formation table, applications, and defects of vision - these are the highest-yield areas for MCQs. Let me know if you want numericals solved or any section expanded!
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