Short Answer Questions — Chapter 2: Optics
Laws of Reflection:
1. First Law: The incident ray, the reflected ray, and the normal to the reflecting surface at the point of incidence all lie in the same plane.
2. Second Law: The angle of incidence (∠i) is always equal to the angle of reflection (∠r).
∠i = ∠r
Note: These laws apply to all types of mirrors — plane, concave, and convex — and to all types of reflecting surfaces.
Refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum to the speed of light in that medium.
Where:
- c = speed of light in vacuum = 3 × 10⁸ m/s
- v = speed of light in the medium
Also written using Snell's Law: n = sin i / sin r
Where i = angle of incidence and r = angle of refraction.
Key points:
- Refractive index has no unit (dimensionless)
- For vacuum/air: n = 1
- For water: n ≈ 1.33
- For glass: n ≈ 1.5
- Higher n means light slows down more in that medium
Snell's Law: When light passes from one medium to another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media.
Mathematically: sin i / sin r = n₂ / n₁ = constant
Or equivalently: n₁ sin i = n₂ sin r
Where:
- i = angle of incidence (in medium 1)
- r = angle of refraction (in medium 2)
- n₁ = refractive index of medium 1
- n₂ = refractive index of medium 2
Note: The incident ray, refracted ray, and normal all lie in the same plane.
Total Internal Reflection (TIR): When light traveling from a denser medium to a rarer medium strikes the interface at an angle greater than the critical angle, no refraction occurs and all the light is reflected back into the denser medium. This phenomenon is called total internal reflection.
Conditions for TIR: 1. Light must travel from a denser medium to a rarer medium (e.g., glass to air) 2. The angle of incidence must be greater than the critical angle (θᵢ > θ_c)
Critical angle (θ_c): The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°.
Applications:
- Optical fibres
- Diamonds (high refractive index → small critical angle → lots of TIR → sparkling effect)
- Periscope prisms
- Mirage formation
Optical fibres work on the principle of total internal reflection and have many important uses:
Medical uses:
- Endoscopy: Doctors use optical fibres (endoscopes) to view internal organs (stomach, intestines) without surgery.
- Illuminating hard-to-reach areas during surgery.
Communication uses:
- Internet and telephone cables: Optical fibre cables transmit data as light pulses at very high speed with minimal signal loss.
- They can carry much more data than copper cables.
- Used in broadband and undersea cable networks.
Industrial uses:
- Inspecting internal parts of machines, engines, and pipes.
- Used in sensors to detect changes in pressure, temperature, and electric field.
Decorative uses:
- Optical fibre lamps and Christmas tree lights.
| Property | Concave Lens | Convex Lens |
|---|---|---|
| Shape | Thinner at centre, thicker at edges | Thicker at centre, thinner at edges |
| Also called | Diverging lens | Converging lens |
| Action on light | Diverges (spreads out) parallel rays | Converges (brings together) parallel rays |
| Focal length | Negative (f < 0) | Positive (f > 0) |
| Power | Negative | Positive |
| Image formed | Always virtual, erect, diminished | Real/virtual depending on object position |
| Uses | Correcting myopia | Correcting hypermetropia, magnifiers, cameras |
Lens Formula: $$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$
Terms:
- f = focal length of the lens (in metres)
- Positive for convex lens, negative for concave lens
- v = image distance (distance from optical centre to image)
- Positive if image is on the other side from the object (real image)
- Negative if image is on the same side as the object (virtual image)
- u = object distance (distance from optical centre to object)
- Always negative (object is placed in front of the lens)
Sign Convention used: New Cartesian Sign Convention
- Distances measured from the optical centre
- Distances in the direction of incident light (forward): positive
- Distances against incident light (backward): negative
Power of a lens is defined as the reciprocal of its focal length in metres.
Where f is in metres and P is in Dioptres.
Unit: Dioptre (D)
Key points:
- Convex (converging) lens: f is positive → Power is positive (+)
- Concave (diverging) lens: f is negative → Power is negative (−)
- A lens with f = 0.25 m has P = +4 D (strong converging)
- A lens with f = −0.5 m has P = −2 D (diverging)
When lenses are combined: The total power = P₁ + P₂ + P₃ + ...
This is why optometrists measure eyeglass prescriptions in Dioptres.
A simple microscope (magnifying glass) consists of a single convex lens of short focal length.
- The object is placed between the focal point F and the optical centre O (i.e., within the focal length).
- The convex lens forms a virtual, erect, and magnified image on the same side as the object.
- The image is formed at the least distance of distinct vision (D = 25 cm from the eye) for maximum magnification.
Magnification:
- When image is at least distance of distinct vision: m = 1 + D/f
- When image is at infinity (relaxed eye): m = D/f
Where D = 25 cm (near point) and f = focal length of the lens.
Uses:
- Watchmakers examining small components
- Jewellers examining gems
- Reading small print
- Simple biology observations
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