Refraction, lens equation, optical power

A lens is most commonly used for refraction imaging. A lens is the simplest optical system. It consists of a transparent medium (most often glass, sometimes plastic) bounded by two refractive surfaces (usually spherical).

There are two types of lenses:

• Converging  : parallel rays intersect at the image focus $\to$ the focus is real (f > 0);
• Diverging  : parallel rays diverge in the image focus; they intersect during retrograde extension at the subject focus$\to$ the focus is virtual (f < 0).

A lens can be:

• Thin : the thickness of the lens is negligible compared to its focal length;
• Thick : the thickness of the lens is not negligible compared to its focal length.

A lens is called thin if its thickness is small compared to the radii of its spherical surfaces. In a homogeneous environment: $f=f'$.

Lens equation

Thick lens

$\left({\frac {n_{2}}{n_{1}}}-1\right)\left({\frac {1}{r_{1}}}+{\frac {1}{r_{2}}}\right)={\frac {1}{f}}$

• n₂ : index of refraction of the lens material n₁ : index of refraction of the surrounding medium;
• r₁ a r₂ : radii of curvature.

lens formula and magnification

Thin lens

${\frac {1}{a}}+{\frac {1}{a'}}=\pm {\frac {1}{f}}$

• a : object distance,
• a‘ : image distance,
• f : focal length.

This equation is valid for both converging and diverging lenses. When substituting the values ​​a , a' we follow the sign convention:

• a > 0 : the object is located in the object space (in front of the lens);
• a < 0 : the object is located in the image space (behind the lens);
• a‘ > 0 : the image is located in the image space; it is real;
• a‘ < 0 : the image is located in the object space; it is virtual.

Optical power

Optical power is a quantity expressing the refractive power of a lens.

Calculation of optical power

$\varphi ={\frac {1}{f}}$

• φ : optical power,
• f : focal length.

Unit: diopter (D) = m -1 ( f must be given in meters!). 1 D is the optical power of a lens with a focal length of 1 m. φ  > 0 applies to converging lenses and φ  < 0 to diverging lenses.

Image formation on ray diagram

(Note: The distance of the object ( x ) from the lens: what is the image)

image formation convex lens

• x > 2f : real, inverted and reduced;
• x = 2f : real, inverted, same size as object;
• x < 2f : real, inverted, magnified;
• x = f : the image is at infinity;
• x < f : apparent, direct, magnified.

In case of a diverging lens, its distance from the lens does not matter. The image is always apparent, direct and reduced.

image formation convex lens

Links

References

SVOBODA, Emanuel. Přehled středoškolské fyziky. - edition. 2005. 531 pp. ISBN 9788071963073.

JIŘÍ, Beneš, – DANIEL, – FRANTIŠEK, Vítek,. Základy lékařské fyziky. - edition. Charles University in Prague, Karolinum Press, 2015. 322 pp. ISBN 9788024626451.