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Class 10 · Chapter 9 · Physics

Light – Reflection and Refraction Cheat Sheet

Formulae

Mirror formula

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

u = object distance, v = image distance, f = focal length (all in metres, with sign).

Magnification of a mirror

m=h′h=−vum = \frac{h'}{h} = -\frac{v}{u}

h′ = image height, h = object height. Negative m means a real, inverted image.

Radius of curvature and focal length

R=2fR = 2f

The radius of curvature R of a spherical mirror is twice its focal length f.

Snell’s law (refractive index)

n21=sin⁡isin⁡rn_{21} = \frac{\sin i}{\sin r}

i = angle of incidence, r = angle of refraction in the second medium.

Absolute refractive index

n=cvn = \frac{c}{v}

c = speed of light in vacuum, v = speed of light in the medium.

Lens formula

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

u, v and f are measured with the new Cartesian sign convention.

Magnification of a lens

m=h′h=vum = \frac{h'}{h} = \frac{v}{u}

Positive m gives an erect image; negative m gives an inverted image.

Power of a lens

P=1fP = \frac{1}{f}

f in metres; P is in dioptre (D). Convex lens P > 0, concave lens P < 0.

Laws

First law of reflection

The angle of incidence is equal to the angle of reflection.

∠i=∠r\angle i = \angle r

Angles are measured with the normal at the point of incidence.

Second law of reflection

The incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane.

This is true for reflection from both plane and spherical mirrors.

Snell’s law of refraction

For a given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.

sin⁡isin⁡r=n21\frac{\sin i}{\sin r} = n_{21}

The constant n₂₁ is the refractive index of the second medium with respect to the first.

Definitions

Reflection
The bouncing back of light into the same medium after striking a surface.
Refraction
The bending of light as it travels from one medium to another because its speed changes.
Concave mirror
A spherical mirror with a reflecting surface that curves inwards; it converges light.
Convex mirror
A spherical mirror with a reflecting surface that curves outwards; it diverges light.
Pole
The centre of the reflecting surface of a spherical mirror.
Centre of curvature
The centre of the sphere of which the mirror forms a part.
Radius of curvature
The radius of the sphere of which the mirror forms a part.
Principal focus
The point on the principal axis where rays parallel to the axis meet (or appear to meet) after reflection.
Focal length
The distance from the pole to the principal focus.
Real image
An image formed by the actual meeting of rays; it can be caught on a screen and is usually inverted.
Virtual image
An image formed when rays only appear to meet; it cannot be caught on a screen.
Magnification
The ratio of the height of the image to the height of the object.
Refractive index
The ratio of the speed of light in vacuum to its speed in the medium.
Optical density
A measure of how much a medium slows light; a denser medium has a higher refractive index.
Lens
A transparent refracting medium bounded by two surfaces, at least one of which is curved.
Power of a lens
The reciprocal of the focal length of a lens, measured in dioptre.

Key Points

  • A concave mirror converges light and is used in torches, headlights and dentist’s mirrors; a convex mirror diverges light and is used as a rear-view mirror because it gives a wide field of view.
  • New Cartesian sign convention: distances are measured from the pole; distances along the incident light are positive and against it are negative; heights above the axis are positive.
  • Concave mirror images: an object between the pole and focus gives an enlarged virtual erect image; beyond the focus gives real inverted images whose size varies.
  • A convex mirror always gives a virtual, erect and diminished image.
  • Refraction occurs because light travels at different speeds in different media; a denser medium slows it down and bends the ray towards the normal.
  • Refractive index values: water 1.33, glass 1.50, diamond 2.42 — the higher the value, the greater the bending.
  • A convex lens converges light and is used in cameras, microscopes and for correcting hypermetropia; a concave lens diverges light.
  • If the magnification is negative the image is real and inverted; if positive the image is virtual and erect.
  • One dioptre is the power of a lens of focal length 1 metre; 1 D = 1 m⁻¹.