Light: Reflection and Refraction Practice Flashcards

Reflection of Light

Definition: Reflection is the bouncing back of light when it hits a polished surface, such as a mirror.
Laws of Reflection:
- The angle of incidence ( $\angle i$ ) is always equal to the angle of reflection ( $\angle r$ ). Equation: $\angle i = \angle r$ .
- The incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane.

Spherical Mirrors

Types of Spherical Mirrors:
- Concave Mirror: A spherical mirror with a reflecting surface that curves inwards (converging mirror).
- Convex Mirror: A spherical mirror with a reflecting surface that curves outwards (diverging mirror).
Key Terminology:
- Pole (P): The geometric center of the reflecting surface of a spherical mirror.
- Centre of Curvature (C): The center of the sphere of which the mirror forms a part.
- Principal Axis (PA): The straight line passing through the pole and the center of curvature.
- Radius of Curvature (R): The radius of the sphere of which the mirror is a part; the distance between $P$ and $C$ .
- Principal Focus (F): The point on the principal axis where rays parallel to the axis meet (concave) or appear to diverge from (convex) after reflection.
- Focal Length (f): The distance between the Pole ( $P$ ) and the Principal Focus ( $F$ ).
Relationship between R and f: For spherical mirrors with small apertures, the radius of curvature is twice the focal length.
- $R = 2f$

Image Formation and Characteristics

An image is formed at the point where at least two rays of light meet (or appear to meet) after reflection or refraction.
Real Image: Formed when rays of light actually meet. These images are inverted and can be caught on a screen.
Virtual Image: Formed when rays of light appear to meet when produced backwards. These images are erect and cannot be caught on a screen.

Image Formation by Concave Mirror: Rules and Cases

Rules for Ray Diagrams:
1. A ray parallel to the principal axis passes through the focus ( $F$ ) after reflection.
2. A ray passing through the focus ( $F$ ) becomes parallel to the principal axis after reflection.
3. A ray passing through the center of curvature ( $C$ ) is reflected back along the same path.
4. A ray incident at the pole ( $P$ ) is reflected such that the angle of incidence equals the angle of reflection relative to the principal axis.
Summary of Cases for Concave Mirror:
- Object at Infinity: Image is at $F$ . Nature: Real and Inverted. Size: Highly diminished (point-sized).
- Object Beyond C: Image is between $F$ and $C$ . Nature: Real and Inverted. Size: Diminished.
- Object at C: Image is at $C$ . Nature: Real and Inverted. Size: Same size as the object.
- Object Between C and F: Image is beyond $C$ . Nature: Real and Inverted. Size: Enlarged (magnified).
- Object at F: Image is at infinity. Nature: Real and Inverted. Size: Highly enlarged.
- Object Between P and F: Image is behind the mirror. Nature: Virtual and Erect. Size: Enlarged.

Uses of Concave Mirrors

Used in car headlights and torches to provide powerful parallel beams of light.
Used by dentists to see larger images of teeth.
Used as shaving mirrors to see a larger image of the face.
Used in solar furnaces to concentrate sunlight to produce intense heat.

Image Formation by Convex Mirror

Rules for Ray Diagrams:
1. A ray parallel to the principal axis appears to diverge from the focus ( $F$ ).
2. A ray directed toward the center of curvature ( $C$ ) is reflected back along the same path.
Summary of Cases:
- Object at Infinity: Image is at focus $F$ behind the mirror. Nature: Virtual and Erect. Size: Highly diminished (point-sized).
- Object at a Finite Distance: Image is formed between $P$ and $F$ behind the mirror. Nature: Virtual and Erect. Size: Diminished.
Uses of Convex Mirrors:
- Used as rear-view mirrors in vehicles because they always give an erect image and provide a wider field of view as they are curved outwards.

Mirror Formula and Magnification

Sign Convention (New Cartesian):
- The object is always placed to the left of the mirror (Object distance $u$ is always negative).
- Distances measured in the direction of incident light ( $+x$ axis) are positive.
- Distances measured against the direction of incident light ( $-x$ axis) are negative.
- Height measured upwards ( $+y$ axis) is positive ( $h_o$ is usually positive).
- Height measured downwards ( $-y$ axis) is negative.
Mirror Formula:
- $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
Magnification (m):
- m = \frac{\text{height of image (h_i)}}{\text{height of object (h_o)}} = -\frac{v}{u}
Interpretation of Magnification:
- If $0 < |m| < 1$ , the image is diminished.
- If $|m| = 1$ , the image is the same size.
- If $|m| > 1$ , the image is enlarged.
- If $m$ is positive: The image is Virtual and Erect ( $V+E$ ).
- If $m$ is negative: The image is Real and Inverted ( $R+I$ ).

Refraction of Light

Definition: Refraction is the bending of light rays when they travel from one medium to another.
Cause: Light travels at different speeds in different media. The speed of light is maximum in vacuum/air ( $c \approx 3 \times 10^8\,m/s$ ).
Rules for Bending:
- Rarer to Denser Medium: Light bends towards the normal.
- Denser to Rarer Medium: Light bends away from the normal.
- Normal Incidence: No bending occurs if the ray is incident perpendicular to the interface.

Refractive Index (R.I.)

Relative Refractive Index: The ratio of the speed of light in medium 1 to the speed of light in medium 2.
- $n_{21} = \frac{v_1}{v_2}$
Absolute Refractive Index (n): The refractive index of a medium with respect to vacuum or air.
- $n = \frac{c}{v}$
- Refractive index of water ( $n_w$ ) and glass ( $n_g$ ) are common examples measured against air.

Refraction through a Rectangular Glass Slab

The emergent ray is parallel to the incident ray ( $\angle i = \angle e$ ).
Lateral Displacement (d): The perpendicular distance between the original path of the incident ray and the emergent ray. It depends on the thickness of the glass slab.

Laws of Refraction

The incident ray, the normal, and the refracted ray at the point of incidence all lie in the same plane.
Snell's Law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media and for light of a given wavelength.
- $\frac{\sin(i)}{\sin(r)} = \text{Constant} = n$

Spherical Lenses

Convex Lens: Thick in the middle and thin at the edges; it is a converging lens.
Concave Lens: Thin in the middle and thick at the edges; it is a diverging lens.
Key Terms:
- Optical Centre (O): The central point of the lens.
- Principal Focus (F): Lenses have two foci ( $F_1$ and $F_2$ ) because they have two curved surfaces.

Image Formation by Lenses

Convex Lens Summary:
- Object at Infinity: Image at $F_2$ . Nature: Real and Inverted. Size: Highly diminished.
- Object Beyond 2F1: Image between $F_2$ and $2F_2$ . Nature: Real and Inverted. Size: Diminished.
- Object at 2F1: Image at $2F_2$ . Nature: Real and Inverted. Size: Same size.
- Object Between 2F1 and F1: Image beyond $2F_2$ . Nature: Real and Inverted. Size: Magnified.
- Object at F1: Image at infinity. Nature: Real and Inverted. Size: Highly magnified.
- Object Between F1 and O: Image on same side as object. Nature: Virtual and Erect. Size: Magnified.
Concave Lens Summary:
- Object at Infinity: Image at $F_1$ . Nature: Virtual and Erect. Size: Highly diminished.
- Object at Finite Distance: Image between $F_1$ and $O$ . Nature: Virtual and Erect. Size: Diminished.

Lens Formula, Magnification, and Power

Lens Formula:
- $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$
Magnification (m):
- $m = \frac{h_i}{h_o} = \frac{v}{u}$
Sign Convention for Focal Length:
- Convex Lens: $f$ is positive ( $+ve$ ).
- Concave Lens: $f$ is negative ( $-ve$ ).
Power of a Lens (P):
- The ability of a lens to converge or diverge light rays.
- Defined as the reciprocal of focal length (in meters).
- $P = \frac{1}{f\,(\text{in m})}$ or $P = \frac{100}{f\,(\text{in cm})}$
- S.I. Unit: Dioptre ( $D$ ).
- Power of Combination: $P = P_1 + P_2 + P_3 + \dots$

Questions & Discussion

Question (Range of Distance for Concave Mirror): To obtain an erect image using a concave mirror of focal length $15\,cm$ , what should be the range of distance of the object?
- Response: The object must be placed between the Pole ( $P$ ) and the Focus ( $F$ ). Therefore, the range is $0\,cm$ to $15\,cm$ . The image will be virtual, erect, and enlarged.
Question (Mirror Types): Identify the mirrors used in:
1. Headlights of a car: Concave mirror (to get a parallel beam).
2. Side/rear-view mirror: Convex mirror (for a wider field of view and erect image).
3. Solar furnace: Concave mirror (to concentrate heat).
Question (Lens Obstruction): If one-half of a convex lens is covered with black paper, will it produce a complete image?
- Response: Yes, it will still produce a complete image of the object. However, the intensity (brightness) of the image will be reduced (approximately $50\%$ fainter) because fewer light rays are participating in image formation.
Numerical Example (Converging Lens): Object size $h_o = 5\,cm$ , $u = -25\,cm$ , $f = +10\,cm$ .
- Using Lens Formula: $\frac{1}{v} - \frac{1}{-25} = \frac{1}{10} \rightarrow \frac{1}{v} = \frac{1}{10} - \frac{1}{25} = \frac{5 - 2}{50} = \frac{3}{50}$ . Thus, $v = \frac{50}{3} \approx 16.67\,cm$ .
- Magnification: $m = \frac{v}{u} = \frac{50/3}{-25} = -\frac{2}{3}$ . The image is real, inverted, and diminished ( $0 < |m| < 1$ ).
Numerical Example (Concave Lens): $f = -15\,cm$ , $v = -10\,cm$ . Find $u$ .
- $\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \rightarrow \frac{1}{-10} - \frac{1}{u} = \frac{1}{-15} \rightarrow \frac{1}{u} = \frac{1}{15} - \frac{1}{10} = \frac{2 - 3}{30} = -\frac{1}{30}$ .
- $u = -30\,cm$ .
Interpretation of Plane Mirror Magnification: $m = +1$ means the image is Virtual and Erect ( $+$ ) and the same size as the object ( $1$ ).
Power Calculations:
- If $P = -2.0\,D$ , $f = \frac{100}{-2.0} = -50\,cm$ . Type: Concave Lens (diverging).
- If $P = +1.5\,D$ , $f = \frac{100}{1.5} \approx 66.67\,cm$ . Type: Convex Lens (converging).