Question

Two convex lenses of focal length 20 cm and 1 cm constitute a telescope.
The telescope is focused on a point which is 1 m away from the objective. Calculate the magnification produced and the length of the tube if the final image is formed at a distance 25 cm from the eyepiece.

Answer 1

Telescope contains two convex lenses e.g., objective and eye lens .
For objective ,
f₀ = 20 cm , u₀ = -100 cm , v₀ = ?
use formula,
1/f₀ = 1/v₀ - 1/u₀
1/20cm = 1/v₀ - 1/-100cm
1/20 = 1/v₀ + 1/100
1/v₀ = -1/100 +1/20 = 4/100 = 1/25
v₀ = 25 cm

Now, magnification = -(v₀/u₀)[1 + D/fₐ]
Here,v₀ = 25cm , u₀ = 100 cm , D = 25cm , fₐ = focal length of eye lens = 1cm
so, magnification = -(25cm/100cm)[1 + 25/1]
= -26/4 = -6.5

Again, for eye lens
fₐ = 1cm , vₐ = -25cm , uₐ = ?
1/fₐ = 1/vₐ - 1/uₐ
1/1cm = 1/-25cm - 1/uₐ
1/1 + 1/25 = -1/uₐ
26/25 = -1/uₐ
1.04 = -1/uₐ
uₐ = -0.96 cm so, |uₐ| = 0.96 cm

Hence, length of tube = |uₐ|+ |v₀| = 0.96 + 25 = 25.96cm

Answer 2

Why haven't we used formula fo/fe*(1+fe/D)?