In an astronomical telescope, the focal lengths of the objective and the eye piece are 100cm and 5cm respectively . If the telescope is focussed on a scale 2m from the objective, the final image is formed at 25cm from the eye. Calculate (i) the magnification and (ii) the distance between the objective and the eyepiece.

In an astronomical telescope, the focal lengths of the objective and t

1.	In an astronomical telescope, the focal lengths of the objective and the eye piece are 100cm and 5cm respectively . If the telescope is focussed on a scale 2m from the objective, the final image is formed at 25cm from the eye. Calculate (i) the magnification and (ii) the distance between the objective and the eyepiece.
Answer» Solution :`f_0=100cm ,f_e=5cm` To find the image distance due to objective `mu_0=-2m=-200cm, v_0=?` For a lens `1/f=1/v-1/u, 1/+100=1/v_0-1/(-200)` `1/v_0=1/100-1/200=1/200, v_0=200cm` MAGNIFICATION of objective `m_0=v_0/v=200/(-200)=-1` To find the object distance for the eyepiece `v_e=-25cm, u_e=?` For a lens `1/f=1/v-1/u,1/(+5)=1/(-25)-1/u` `1/u_e=-1/25 -1/5=- 6/25, u_e=- 25/6cm` Magnification of the eyepiece `m_e=v_e/u_e= (-25 TIMES 6)/(-25)=6` (i) Magnification of the telescope `=m_0 times m_e=-1 times 6=-6` (II) Distance between the objective and the eyepiece= `v_0+\|u_e\|=200+25/6 =204.2cm`