Optics Formula

Optics is an important part of physics. It used in widely in everyday applications like making spectacles to correct vision. So it is important to study it. Let us look into some important optics formula.

History of Optics

Ancient Indians, Egyptians, Greeks and Romans had all developed theories on optics. Lenses were also made by them. During the medieval ages the Arabians, English were pioneers in developing theories on the speed of light and its study. During the 16th and 17th century, Huygens, Newton developed their own theories on the nature of light its behaviour and contributed to the growth of the field. Eventually, the study of light and measurement of its speed played an important role in dispelling false theories like the presence of ether etc. Quantum physics and can find its origins in the study of optics.

Important Optics Formula

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 ^aμ_c = ^aμ_b x ^bμ_c

Conditions for total internal reflection:

The light should travel from denser to rarer medium.

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

Refraction at a spherical refracting surface

Rarer to a denser medium

-μ₁/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

-μ₂/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 the 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 = h_i/h_o = 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

Magnifying power

Simple microscope

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

Compound microscope

The ratio of the 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 the objective

f_e is the focal length of the eyepiece

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 the 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 wavelength of light

Laws of reflection

Angle i = angle r

The 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 = h_i/h_o= -v/u

Solved Examples for Optics Formula