Physics > Refraction of Light > 5.0 Lens makers formula & Other Functions of lens.
Refraction of Light
1.0 Introduction
2.0 Laws of refraction
3.0 Apparent shift of an object
4.0 Thin lenses
4.1 Sign convention
4.2 Some important terms
4.3 Ray tracing
4.4 Image formed by covex lens
4.5 Image formed by concave lens
5.0 Lens makers formula & Other Functions of lens.
5.1 Thin Lens Formula
5.2 Magnification and Power of lens
5.3 Combination of lenses
5.4 Displacement method to find focal length.
5.5 Silvering of lens
6.0 Total internal reflection
7.0 Refraction through prism
8.0 Scattering of light
9.0 Optical instruments
9.1 Spectrometer
9.2 Simple microscope
9.3 Compound microscope
9.4 Astronomical telescope (Refracting type)
9.5 Terrestrial telescope
9.6 Galileo's terrestrial telescope
9.7 Reflecting type telescope
5.3 Combination of lenses
4.2 Some important terms
4.3 Ray tracing
4.4 Image formed by covex lens
4.5 Image formed by concave lens
5.2 Magnification and Power of lens
5.3 Combination of lenses
5.4 Displacement method to find focal length.
5.5 Silvering of lens
9.2 Simple microscope
9.3 Compound microscope
9.4 Astronomical telescope (Refracting type)
9.5 Terrestrial telescope
9.6 Galileo's terrestrial telescope
9.7 Reflecting type telescope
- When the lenses are in contact
When a number of thin lenses of focal length $f_1$, $f_2$ . . . etc are placed in contact coaxially, then the equivalent focal length $F$ of the combination is given by,
$$\frac{1}{F} = \frac{1}{{{f_1}}} + \frac{1}{{{f_2}}} + \frac{1}{{{f_3}}}+...$$
So, the total power of the combination is given by,
$$P = {P_1} + {P_2} + {P_2} + ...$$
The total magnification of the combination is given by,
$$m = {m_1} \times {m_2} \times {m_3} \times ...$$
- When the two lenses are separated by a distance $d$
When two thins lenes of focal length $f_1$ and $f_2$ are placed coaxially and separated by a distance $d$, the focal length of a combination is given by,
$$\frac{1}{F} = \frac{1}{{{f_1}}} + \frac{1}{{{f_2}}} - \frac{d}{{{f_1}\;{f_2}}}$$
The above equation in terms of power, it can be written as,
$$P = {P_1} + {P_2} - d{P_1}{P_2}$$
Note: Distance $(d)$ between the lenses should be less than the focal length of the first lens.
