Relation between the radius of curvature (r) and the focal length (f) of a spherical mirror for paraxial rays:
r = 2f or, f = r/2
Images formed by a concave mirror :
| Position of the object | Position of the image | Â Size of the image | Nature of the image |
| At infinity | At the focus | Highly diminished | Real and Inverted |
| Beyond C | Between F and C | Diminished | Real and Inverted |
| At C | At C | Same size | Real and Inverted |
| Between C and F | Beyond C | Magnified | Real and Inverted |
| At F | At infinity | Highly Magnified | Real and Inverted |
| Between P and F | Behind the mirror | Magnified | Virtual and erect |
Images formed by a convex mirror :
| Position of the object | Position of the image | Size of the image | Name of the image |
| At infinity | At the focus, F | Highly diminished | Virtual and erect |
| Anywhere between infinity and pole | Between F and pole | Diminished | Virtual and erect |
Snell’s law:
When a light ray enters into the second medium from the first medium, then the refractive index (R.I) of the second medium with respect to the first medium is given by
1μ2 = sin\ i\over sin\ r [\katex]
Wave theory of light :
Absolute R.I of a medium,
μ = Velocity\ of\ light\ in\ vacuum\ (or\ air)\over Velocity\ of\ light\ in\ the\ medium[\katex]
Principle of reversibility of light :
When a ray after refraction, retraces its path, then 1µ2 = 1/ 2µ1
(where a is the rarer and b is the denser medium)
Real and apparent depth:Â
When an object is situated in an optically denser medium 2, then when viewed normally from the rarer medium 1
- 1µ2 = Real\ depth\over Apparen\ depth[\katex]
- Shift = Real depth (1 - 1/1µ2)
Refraction through optical slabs :
- The incident ray is parallel to the emergent ray
- The angle of incidence is equal to the angle of emergence
Refraction through prism :
- δ = δ1 + δ2
- δ = i1 + i2 - (r1 + r2)
- r1 + r2 = A
- δ = i1 + i2 - A
Notation meaning
- δ = Angle of deviation
- i1 = Angle of incidence
- i2 = Angle of emergence
- r1 = Angle of refraction on the first surface
- r2 = Angle of refraction on the first surface
- A = Angle of prism
Images formed by the convex lens :
| Position of the object | Position of the image | Â Size of the image | Nature of the image |
| At infinity | At the focus | Highly diminished | Real and Inverted |
| Beyond 2F1 | Between F2 and 2F2 | Diminished | Real and Inverted |
| At 2F1 | At 2F2 | Same size | Real and Inverted |
| Between 2F1 and F1 | Beyond 2F2 | Magnified | Real and Inverted |
| At F1 | At infinity | Highly Magnified | Real and Inverted |
| Between P and F1 | On the same side of the lens as the object | Magnified | Virtual and erect |
Images formed by a concave lens :
| Position of the object | Position of the image | Size of the image | Name of the image |
| At infinity | At the focus, F2 | Highly diminished | Virtual and erect |
| Anywhere in front of lens | Between F2 and O | Diminished | Virtual and erect |
Linear magnification :
- Linear magnification (m) = Linear\ size\ of\ the \ image\ (I)\over Linear\ size\ of\ the \ object\ (O)[\katex]
- Linear magnification (m) = Distance\ of\ the\ image\ from\ the\ lens\ (v)\over Distance\ of\ the\ object\ from\ the\ lens\ (v) [\katex]
Power of lens:
Power = 1\over focal\ length\ (in\ metre) [\katex]
Relation among speed (c), wavelength (λ) and frequency (v) of light wave:
c = v.λ