Refraction in spherical surface

n1a+n2b=n2−n1R\frac{n_1}{a} + \frac{n_2}{b} = \frac{n_2 - n_1}{R}

Gauss Formula

1a+1b=1f\frac{1}{a}+\frac{1}{b} = \frac{1}{f}

Lateral Enlargement

M≡ybya         M=−baM \equiv \frac{y_b}{y_a} \,\,\,\,\,\,\,\,\ M = -\frac{b}{a}

Focal Length Curved Mirror

f=−R2f = -\frac{R}{2}

Refractive Power (Lens)

B≡1f=(n−1)[1R1−1R2]B \equiv \frac{1}{f} = (n-1)\left[\frac{1}{R_1}-\frac{1}{R_2}\right]

Lens

Lens with refractive index

n1n_1

in medium with refractive index

n2n_2

:

B≡1f=[n1n2−1]⋅[R2−R1R1⋅R2]B \equiv \frac{1}{f} = \left[ \frac{n_1}{n_2}-1 \right] \cdot \left[ \frac{R_2-R_1}{R_1\cdot R_2} \right]

Aparture Number

bt≡fDb_t \equiv \frac{f}{D}

Depth of Field

s≈a21000fbts \approx \frac{a^2}{1000 f}b_t

Angular Magnification of Magnifier

G=d0f   where,     d0=25 cmG = \frac{d_0}{f}\,\,\,\textup{where},\,\,\,\,\ d_0=25\,\textup{cm}

Angular Magnification of Microscope

G=∣Mob∣⋅Gok=Lfobd0fokG = |M_{ob}|\cdot G_{ok} = \frac{L}{f_{ob}}\frac{d_0}{f_{ok}}
where the tube length L=16 cm\textup{where the tube length}\, L=16\, \textup{cm}

Angle magnification of the Kepler and Galileo binoculars

G=∣fobfok∣G = \left| \frac{f_{ob}}{f_{ok}} \right|

Refraction in a spherical surface

Positive if: C is to the right of O Positive if: A is to the left of O Positive if: B is to the right of O Positive if: F

A_A

is to the left of O Positive if: F

B_B

is on the right of O Image with thin lens in air Positive if: the lens is convex (gathers light) Positive if: the object is to the left of the lens Positive if: the image is to the right of the lens Positive if: the object is above the optical axis Positive if: the image is above the optical axis Positive if: the image is upside up Image with a curved mirror Positive if: C is to the right of O (convex) Positive if: F is to the left of O (concave) Positive if: A is to the left of O Positive if: B to the left of O Positive if: the image is upside up

Refractive Index for Some Materials

Refractive Index with

λ=589\lambda = 589

\,nm at 20

∘^\circ

C:

Water1,333Diethyl Ether1,353Ethanol1,361Glycerin1,455Benzene1,501Carbon Sulfur1,628Is (0∘C)1,31NaCl1,544Polystyrene1,59Crown Glass (FK5)1,487Crown Glass (BK7)1,517Canada balsam1,542Flint Glass (F2)1,620Flint Glass (SF10)1,728Flint Glass (SFS1)1,922Quarts1,458Plexiglass1,49−1,52Diamond2,417\def\arraystretch{1.5} \begin{array}{|c|c|} \hline \textup{Water} & 1,333 \\ \textup{Diethyl Ether} & 1,353 \\ \textup{Ethanol} & 1,361 \\ \textup{Glycerin} & 1,455 \\ \textup{Benzene} & 1,501 \\ \textup{Carbon Sulfur} & 1,628 \\ \textup{Is (0$^\circ$C)} & 1,31 \\ \textup{NaCl} & 1,544 \\ \textup{Polystyrene} & 1,59 \\ \textup{Crown Glass (FK5)} & 1,487 \\ \textup{Crown Glass (BK7)} & 1,517 \\ \textup{Canada balsam} & 1,542 \\ \textup{Flint Glass (F2)} & 1,620 \\ \textup{Flint Glass (SF10)} & 1,728 \\ \textup{Flint Glass (SFS1)} & 1,922 \\ \textup{Quarts} & 1,458 \\ \textup{Plexiglass} & 1,49 - 1,52 \\ \textup{Diamond} & 2,417 \\ \hline \end{array}