Principal of CRT

 Electrostatic focusing system in CRT :

In Electrostatic Focusing ,Electrostatic lens consists of three anodes, with the middle anode at a lower potential than the other two electrodes.An electrostatic focusing system is shown in figure.

In figure two anodes and its electrostatic lines and equipotential surfaces are shown. 

Potential difference is kept between these two electrodes so that an electric field is generated between them. Spreading of electric field is caused because of repulsion between electric lines. 
If equipotential lines are drawn, as shown in figure, they would bulge at the centre of the two anodes.  as  know that electrons move in a direction opposite to that of electric field lines and equal-potential surfaces are perpendicular to the electric field lines so force on the electron is exerted in the direction normal to the equipotential surface

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As shown in figure,Electrons entering at the center line of the two anodes experience no force but electrons displaced from the center line experience a force normal to the direction of equi-potential surface and deflect. 

 An equi-potential surface is shown, in which an electron with velocity V₁ and at an angle θ. to the normal of equi-potential surface enters and experiences a force in a direction normal to the equi-potential surface. Thus the velocity of the electron increases to V₂. This force on the electron is exerted in the direction normal to equi-potential surface so only the normal component of electron velocity V_1N increases to V_2N and the tangential component of velocity V_1T remains the same.

 

V_1T = V₁ sin _θ1,

                                      V_2T = V₂ sin _θ2

                                But V_1T = V_2T

V₁ sin _θ1 = V₂ sin _θ2

                            Or 
            V₂/V₁ = sin _θ1 / sin _θ2

Equipotential surface acts as a concave lens in geometrical optics. That is why, this focusing system is name an electrostatic lens. 

Now if we go back and refer figure, 

it can be seen that because of middle anode to a lower potential, electron beam coming from the cathode and passing through the first concave electrostatic lens tends

 to become more aligned with the axis of CRT and when 

it enters at the second concave electrostatic lens, 

formed between two anodes at different potentials, it 

is focused at the phosphor screen. 

 Focal length of the electrostatic lens can lie adjusted

by varying potential of middle anode with respect 

too ther two anodes.

Thus very precisely,electron beam can be made to focus at 

  the screen .