optics

speed of light

c=f\lambda

c=\frac{\omega}{k}

How are magnetic field strength and electric field strength related

E=Bc

How are angle of incidence and angle of reflection related

\theta_{i}=\theta_{r}

(even in diffuse reflection)

Refractive index

n=\frac{c}{v}

If n_{2_{}}>n_1 then light bends towards normal

Snells law (on formula sheet)

n_{i}\sin\theta_{i}=n_{r}\sin\theta_{r}

Critical angle

\sin\theta_{c}=\frac{n_2}{n_1}

n_2<n_1

F number

f-number=\frac{f}{D}=\frac{1}{2NA}

where f is the focal length and D the diameter of the lens

Numerical aperture

NA=n\sin\alpha

Image magnification (on formula sheet)

M=\frac{h_{i}}{h_{o}}=-\frac{d_{i}}{d_{o}}

M_{System}=M_1\cdot M_2

focal length

f for converging

-f for diverging

lensmakers equation

\frac{1}{f}=(\frac{n_{g}-n}{n})(\frac{1}{r_1}-\frac{1}{r_2})

where n_{g} is the refractive index of the lens material

r_1 is the radius of curvature of the front face of the lens and r_2 the back face

radius of curvature sign

r is positive if the centre of the circle formed by the lens is to the right

r is negative if it is to the left

thin lens equation (on formula sheet)

\frac{1}{f}=\frac{1}{d_{o}}+\frac{1}{d_{i}}

Malus’s Law (on formula sheet)

I=I_0\cos^2\theta

where the angle is the angle of the polarising filter from the vertical

E=E_0\cos\theta will be the amplitude of the wave

Intensity of a wave

I=\frac{I_0}{2}

Brewster’s angle (for polarisation by reflection)

\tan\theta_{p}=\frac{n_2}{n_1}

path length difference

\Delta L=d\sin\theta

diffraction

d\sin\theta=m\lambda

d is distance between slits

m is order of maxima/minima

for destructive interference use m+1/2

beam width

D=Nd\cos\theta

D is beam width

N is number of slits

d is distance between slits

angular spreading of the beam

\Delta\theta=\frac{\lambda}{D}

Resolving power of diffraction grating

\frac{\lambda}{\Delta\lambda}=mN

N IS THE NUMBER OF SLITS USED NOT TOTAL NUMBER