Power Lens

Author: johnharmer

Power of a lens

The power of a lens is its ability to converge or diverge the incident beam of light and is defined as the reciprocal of its focal length. Thus, P = \/f

Diptre is the unit of power. The power of a lens is said to be one dioptre (ID) if its focal length is one metre.

P(dioptre) =-?--

f(metre)

The power of a convex lens is positive while that of a concave lens is negative.

From lens maker's formula, — = (n-l)j — + — I

f I/?, R2 J

1 n-1 n-1 . „ n-1 n-1 i.e., - =-+- i.e., P =-+-

f R\ R2 R\ R2

Now, (n-l)//?] is the power of first refracting surface = P, and (n-])/R2 is the power of the second refracting surface = Pz

¦¦ P = Pi + Pz

Thus, power of a lens is the sum of the powers of its surfaces.

Magnification

When a linear object is placed perpendicular to the principal axis of lens, a linear image perpendicular to the principal axis is formed due to refraction through the lens. The position, size and nature of the image depend on the lens and position of the object with respect to the lens.

The ratio of the linear size of the image to the linear size of the object is defined as linear magnification of the image of the object formed due to refraction through the lens. It is denoted by'm'

linear size of image / Thus, m =--— -

linear size of object 0

In all cases of image formation due to refraction through a lens, it can be proved that

image distance v

m =- = —.

object distance u

I v

Thus, m = —

0 u

The object distance (u), the image distance (u) and the focal length (/) of a lens are related by lens equation. Accordingly

I + i-i

u v f

Using the lens equation it can be proved that

f v-f m =- and m =-.

u-f f

Note :

'm' is positive for a real image and negative for a virtual image.


Introduction to Photoelectric Effect Intensity:

It is the phenomenon of emission of electrons from the surface of metals when the radiations of suitable frequency and suitable wavelength if falling on the surface of the metal. The emitted electrons are called photo electrons and the current so produced is called as the photoelectric current. The intensities of photo electrons vary with material.

emission of electrons

photoelectric electrons

Materials that emit Photoelectrons

Different materials emit photo electrons when they are exposed to radiations of suitable frequencies or wavelengths. The whole range of the electromagnetic radiations from the ?–rays and the x–rays to the ultraviolet and the visible and the infrared rays produce this effect. For example the alkali metals like the lithium and sodium and potassium and cesium etc. show the photoelectric current with the visible light whereas the metals like the zinc and cadmium and magnesium etc. are sensitive only to the ultraviolet light.

Photoelectric effect was discovered by Heinrich Hertz in 1887. Further experimental study was undertaken by Hallwachs in 1888. Then in 1899 Lenard showed that the carriers of electricity emitted from a metal surface under the action of the ultraviolet light were the electrons and Einstein explains it successfully by the theoretical evidences.

Image of photoelectric emission on sodium

image of photoelectric emission on sodium

Effect of the Intensity of the Incident Light

The surface of the metal plate is illuminated by the monochromatic ultraviolet light. The accelerating potential difference between the metal electrodes is increased till the photoelectric current is maximum and this current is due to the flow of the photo electrons emitted per second from the surface of the metal. The experiment is repeated for different known intensities of the incident light and the variation of the photoelectric current with the intensity of the incident light is shown in the fig.1 which is a straight line.

Intensity verses photoelectric current

Fig.1 Intensity verses photoelectric current

Conclusion for the Intensity of Photoelectric Effect

From the discussion we had on the intensity of photoelectric effect on matter, we conclude that the straight line graph shows the number of  photoelectrons emitted per second by any metal surface is directly proportional to the intensity of the incident light i.e. if we need the large photoelectric current then the intensity of the incident light should be large.

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