When two thin lenses of focal lengths f1 and f2 are kept in contact, prove that their combined focal length 'f' is given by
Consider two thin lenses L1 and L2 of focal lengths f1 and f2 are placed in contact with each other. Suppose that a point object O lies on the principal axis of the two lenses.
shows the formation of the final image I of the object O is two steps. In the first step, the lens L1 produces I’ as the real image of the object O. If C1 O = u and C1 I’ = v’, then for lens L1 ,we have
C2I' ≈ C1I' = +u'
The positive sign has been taken for the reason that the distance of image I’ from C2 is measured in the direction of incident ray. If C2 I = v, then the focal length of lens is given by,
If a single lens of focal length f produces the image I of the object O exactly as the lenses L1 and L2 together do, then
From equation (3), we have
Here, f is called focal length of the equivalent lens.
An electron beam passes through crossed electric and magnetic fields of 3.4 x 104 Vm-1 and 2 x 10-3 Wb mr-2 respectively. If the path of the beam remains undeviated, calculate the speed of the electrons.
If the electric field is removed, what will be the radius of the circular path described by the electrons ?
Draw the energy level diagram of a hydrogen atom; and draw arrows to show transitions responsible for:
(i) Absorption lines of Lyman series.
(ii) Emission lines of Balmer series.
In photo-electric effect, what is meant by the terms :
(i) Work function of a metal
(ii) Stopping potential.