The phenomenon of change in the path of light when it passes from one medium to another

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

Sin i / Sin r = μ [refractive index of the second medium with respect to the first medium]

Also μ = c/v or v_{1}/v_{2}

μ = Real depth / Apparent depth

Light enters medium a, crosses medium b and then leaves from medium c, then
^{a}μ_{c} = ^{a}μ_{b} x ^{b}μ_{c}

When light travelling from denser to rarer medium is incident at an angle greater than the critical angle, it is reflected back in the denser medium.

Light should travel from denser to rarer medium.

Angle i > angle i_{c} where i_{c} is the critical angle.

When light travels from denser to rarer medium, then that angle of incidence for which
angle of refraction is 90^{o}

-μ_{1}/u + μ_{2}/v = (μ_{2} - μ_{1})/R

where μ_{1} and μ_{2} are refractive indices of rarer and denser mediums respectively

R is the radius of curvature of the spherical surface.

-μ_{2}/u + μ_{1}/v = (μ_{1} - μ_{2})/R

1/f = (μ - 1)(1/R_{1} - 1/R_{2})

Where μ is the refractive index of material of the lens

R_{1} and R_{2} are the radii of curvature of the two surfaces of the lens.

1/v - 1/u = 1/f

m = h_{i}/h_{o} = v/u

P = 1/f if f is in meters Units of P: Dioptre D

1/F = 1/f_{1} + 1/f_{2} => P = P_{1} + P_{2}
and m = m_{1} x m_{2}

1/F = 1/f_{1} + 1/f_{2} - d/f_{1}f_{2}

δ = (μ - 1) A for A < 10^{o} (thin prism)

δ = (i_{1} + i_{2}) - A for A > 10^{o}

here i_{1} and i_{2} are angles of incidence and emergence

δ_{v} - δ_{r} = (μ_{v} - μ_{r})A

A + δ = i + e

μ = (Sin(A + δ_{m}/2)) / Sin A/2

where δ_{m} is angle of minimum deviation

w = Angular dispersion/Mean dispersion = (μ_{v} - μ_{r})/(μ - 1)

v and r refer to violet and red colors

μ refers to mean color wavelength (yellow)

m = 1 + D/f where D = least distance of distinct vision = 2.5 cm

The ratio of angle subtended at the eye by the final image to the angle subtended at the eye by the object where both the final image and object are situated at the least distance of distinct vision.

m = L/f_{o}[1 + (D/f_{e})]

L is the length of the microscope tube

f_{o} is the focal length of objective

f_{e} is the focal length of the eye piece

The final image is formed at infinity

Magnifying power of an astronomical telescope in normal adjustment is defined as the ratio of the angle subtended at the eye by the final image to the angle subtended at the eye by the object directly when the final image and the object both lie at infinite distance from the eye.

m = f_{o}/-f_{e}

It is defined as the ratio of the angle subtended at the eye by the final image at the least distance of distinct vision to the angle subtended at the eye by the object at infinity, when seen directly

m = (f_{o}/f_{e})(1 + f_{e}/D)

m = f_{o}/f_{e} = (R/2)/f_{e}

Resolving power = 1/d = (2μSinθ)/λ

where μ is the refractive index of the medium

λ is the wavelength of light

θ is half angle of the cone of light from thee point object to the objective lens

Resolving power = 1/dθ = D/1.22λ

where D is the diameter of the object lens

λ is the wave length of light

Angle i = angle r

Incident ray, reflected ray and the normal at the point of incidence all lie in the same plane

1/v + 1/u = 1/f

m = h_{i}/h_{o}= -v/u