Thick lens and its cardinal points | Optics | General theory of image formation

Thick lens and its cardinal points

Thick lens

• The combination of two spherical surfaces, is known as thick lens, if the distance between their poles can not be neglected in comparison to their radii.
• It can be treated as the combination of thin lenses.
• The thickness of these lenses are comparable to their focal lengths.

Cardinal points of thick lens

• Let µ = refractive index of material of lens
• t = thickness of lens
• R₁ and R₂ = Radii of curvature of first and second curved surface of the given thick lens.
• F₁ and F₂ = First and second focal points respectively.
• H₁ and H₂ = First and second principal points respectively.
• f₁ and f₂ = First and second focal length of thick lens respectively.

Cardinal points of thick lens

Equivalent focal length

• If there is same medium on either side of thick lens
• H₁F₁ = f₁ = - f , and H₂F₂ = f₂ = f

Refraction from surface PP₁

Refraction from surface QP₂

• This time I works as an object and forms final image is obtained at F₂

• For thin lens t → 0, and f → f₀

Power of thick lens

Position of second focal point (P₂F₂ = β₂)

• The distance of second focal point will be measured from pole of second refracting surface.

Position of second principal point (P₂H₂ = α₂)

 

• The distance of second principal point will be measured from pole of second refracting surface

• Above result is obtained using sign convention.

Position of first focal point (P₂F₁ = β₁)

 

• For obtaining it we consider that the ray is incident on lens system from right i.e., O՛Q, this time image will be formed on F₁. So in β₂, R₁ is replaced by -R₂ and f is replaced by -f.

Position of first principal point (P₁H₁ = α₁)

 

• For it we use R₁ → –R₂ and  f → – f in second principal point α₂ 

• To know more about thick lens and the cardinal points of thick lens please visit on https://youtu.be/4dI1HQjx_7U or https://youtu.be/-sMQRofa0Fc