Ray optics formulas

Refraction

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

Laws of refraction

First

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

Second

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

Also μ = c/v or v1/v2

μ = Real depth / Apparent depth

Light enters medium a, crosses medium b and then leaves from medium c, then aμc = aμb x bμc

Total internal reflection

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.

Conditions for total internal reflection

Light should travel from denser to rarer medium.

Angle i > angle ic where ic is the critical angle.

Critical angle

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

Refraction at spherical refracting surface

Rarer to denser medium

1/u + μ2/v = (μ2 - μ1)/R

where μ1 and μ2 are refractive indices of rarer and denser mediums respectively

R is the radius of curvature of the spherical surface.

Denser to rarer medium

2/u + μ1/v = (μ1 - μ2)/R

Lens maker's formula

1/f = (μ - 1)(1/R1 - 1/R2)

Where μ is the refractive index of material of the lens

R1 and R2 are the radii of curvature of the two surfaces of the lens.

Lens formula

1/v - 1/u = 1/f

Linear magnification

m = hi/ho = v/u

Power of a lens

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

Combination of two thin lenses

Lenses in contact

1/F = 1/f1 + 1/f2 => P = P1 + P2 and m = m1 x m2

Lenses separated by a finite distance

1/F = 1/f1 + 1/f2 - d/f1f2

Refraction through a prism

Angle of deviation

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

δ = (i1 + i2) - A for A > 10o

here i1 and i2 are angles of incidence and emergence

Angular dispersion

δv - δr = (μv - μr)A

A + δ = i + e

Prism formula

μ = (Sin(A + δm/2)) / Sin A/2

where δm is angle of minimum deviation

Dispersive power

w = Angular dispersion/Mean dispersion = (μv - μr)/(μ - 1)

v and r refer to violet and red colors

μ refers to mean color wavelength (yellow)

Magnifying power

Simple microscope

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

Compound microscope

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/fo[1 + (D/fe)]

L is the length of the microscope tube

fo is the focal length of objective

fe is the focal length of the eye piece

Astronomical telescope

Normal adjustment

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 = fo/-fe

Final image at least distance of distinct vision

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 = (fo/fe)(1 + fe/D)

Cassegrainian reflecting type telescope

m = fo/fe = (R/2)/fe

Resolving power of a microscope

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 of a telescope

Resolving power = 1/dθ = D/1.22λ

where D is the diameter of the object lens

λ is the wave length of light

Laws of reflection

Angle i = angle r

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

Mirror formula

1/v + 1/u = 1/f

m = hi/ho= -v/u

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