Class 10 Science Notes Chapter 9 — Light: Reflection and Refraction#

Reflection#

Laws of reflection:

  1. The angle of incidence equals the angle of reflection ($\angle i = \angle r$).
  2. The incident ray, the normal at the point of incidence and the reflected ray all lie in the same plane.

These laws hold for all reflecting surfaces, including curved ones.

Plane mirror image: virtual, erect, the same size as the object, as far behind the mirror as the object is in front, and laterally inverted.

Spherical mirrors#

  • Concave mirror — reflecting surface curved inwards (converging). Convex mirror — curved outwards (diverging).
  • Pole (P) — centre of the mirror’s surface. Centre of curvature (C) — centre of the sphere it is part of. Radius of curvature (R) — distance PC.
  • Principal axis — line through P and C. Principal focus (F) — point where rays parallel to the axis meet (concave) or appear to come from (convex) after reflection. Focal length (f) — distance PF. Aperture — diameter of the reflecting surface.
$$R = 2f$$

Rules for ray diagrams:

  1. A ray parallel to the principal axis passes through (or appears to come from) F after reflection.
  2. A ray through (or towards) F becomes parallel to the principal axis.
  3. A ray through (or towards) C is reflected back along the same path.
  4. A ray hitting P obliquely is reflected at an equal angle on the other side of the axis.

Concave mirror images#

Object at Image at Size Nature
Infinity F Highly diminished, point-sized Real, inverted
Beyond C Between F and C Diminished Real, inverted
C C Same size Real, inverted
Between C and F Beyond C Enlarged Real, inverted
F Infinity Highly enlarged Real, inverted
Between P and F Behind the mirror Enlarged Virtual, erect
PFCObjectImage
Concave mirror, object beyond C: the image is between F and C, real, inverted and diminished.

Uses: torches, searchlights and vehicle headlights (parallel beam), shaving mirrors (enlarged erect image), dentists’ mirrors, solar furnaces (concentrate sunlight).

Convex mirror images#

Object at Image at Size Nature
Infinity F, behind the mirror Highly diminished Virtual, erect
Between infinity and P Between P and F, behind the mirror Diminished Virtual, erect

Uses: rear-view mirrors in vehicles, because they always give an erect image and a wider field of view.

Sign convention and formulas#

New Cartesian sign convention:

  • The object is always placed to the left of the mirror or lens, so light goes from left to right.
  • All distances are measured from the pole (mirror) or optical centre (lens).
  • Distances in the direction of incident light (to the right) are positive; against it (to the left) are negative.
  • Heights above the principal axis are positive; below are negative.

Mirror formula:

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

Magnification (mirror):

$$m = \frac{h'}{h} = -\frac{v}{u}$$
  • $u$ is always negative. A concave mirror has negative $f$; a convex mirror has positive $f$.
  • Negative $m$ → real image; positive $m$ → virtual image. $|m| > 1$ means enlarged.

Refraction#

  • Refraction — bending of light when it passes from one medium to another, because its speed changes.
  • Light going from a rarer to a denser medium bends towards the normal; from denser to rarer, it bends away from the normal.
  • Through a rectangular glass slab, the emergent ray is parallel to the incident ray but shifted sideways (lateral displacement).

Laws of refraction:

  1. The incident ray, the refracted ray and the normal lie in the same plane.
  2. Snell’s law: for a given pair of media and a given colour of light, $$\frac{\sin i}{\sin r} = \text{constant}$$ This constant is the refractive index of the second medium with respect to the first.

Refractive index:

$$n_{21} = \frac{\text{speed of light in medium 1}}{\text{speed of light in medium 2}} = \frac{v_1}{v_2}$$

$$n_m = \frac{\text{speed of light in vacuum}}{\text{speed of light in the medium}} = \frac{c}{v}$$
  • $c = 3 \times 10^8$ m/s. A medium with a higher refractive index is optically denser. Optical density is not the same as mass density.
  • Some values: water 1.33, kerosene 1.44, crown glass 1.52, diamond 2.42 (highest in the NCERT table).

Spherical lenses#

  • Convex lens — thicker in the middle; converging. Concave lens — thinner in the middle; diverging.
  • Optical centre (O) — the centre of the lens; a ray through it goes straight on. A lens has two principal foci, $F_1$ and $F_2$.

Convex lens images#

Object at Image at Size Nature
Infinity F₂ Highly diminished Real, inverted
Beyond 2F₁ Between F₂ and 2F₂ Diminished Real, inverted
2F₁ 2F₂ Same size Real, inverted
Between F₁ and 2F₁ Beyond 2F₂ Enlarged Real, inverted
F₁ Infinity Highly enlarged Real, inverted
Between F₁ and O Same side as object Enlarged Virtual, erect
2F₁F₁OF₂2F₂ObjectImage
Convex lens, object beyond 2F₁: the image is between F₂ and 2F₂, real, inverted and diminished.

Concave lens images#

Object at Image at Size Nature
Infinity F₁ Highly diminished Virtual, erect
Between infinity and O Between F₁ and O Diminished Virtual, erect

Lens formula:

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

Magnification (lens):

$$m = \frac{h'}{h} = \frac{v}{u}$$
  • A convex lens has positive $f$; a concave lens has negative $f$.

Power of a lens#

$$P = \frac{1}{f}$$
  • $f$ must be in metres. The unit is the dioptre (D): 1 D is the power of a lens of focal length 1 m.
  • Convex lens: positive power. Concave lens: negative power.
  • For lenses in contact: $$P = P_1 + P_2 + P_3 + \cdots$$

Common mistakes#

  • Mixing the formulas: the mirror formula has a + sign ($\frac{1}{v} + \frac{1}{u}$); the lens formula has a − sign ($\frac{1}{v} - \frac{1}{u}$).
  • Magnification: mirror $m = -\frac{v}{u}$, lens $m = \frac{v}{u}$.
  • Taking $u$ as positive. With the object on the left, $u$ is negative.
  • Using $f$ in cm when finding power. Convert to metres first.
  • Saying light bends towards the normal when entering a rarer medium. It bends away.

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