Two converging lenses having power of +2.0 and +20.0 diopter are used to give magnifications in an astronomical telescope. calculate the angular magnification of the telescope when (I).in normal adjustment.
(ii).The final image is formed at the least distance of distinct vision (25cm).
(a)3.5;(b)2.5.
To calculate the angular magnification of the telescope in normal adjustment, we need to consider the formula for angular magnification:
Angular magnification (M) = Objective lens angular magnification (M_o) * Eyepiece angular magnification (M_e)
Given:
Objective lens power = +2.0 diopter
Eyepiece power = +20.0 diopter
To find the angular magnification for the different cases, let's calculate the angular magnification using the formula.
(I) Normal Adjustment:
In normal adjustment, the final image is formed at infinity. Therefore, the objective lens angular magnification is infinite (M_o = ∞).
M_e (Eyepiece angular magnification) can be calculated using the formula:
M_e = 1 + (D_f / D_o)
Where:
D_f is the final image distance formed by the objective lens.
D_o is the distance of distinct vision (25cm).
Since the final image is formed at infinity, D_f can be considered as ∞ in this case.
M_e = 1 + (∞ / 25) = 1 + 0 = 1
Angular magnification (M) = M_o * M_e
Since M_o = ∞,
M = ∞ * 1 = ∞
Therefore, the angular magnification of the telescope in normal adjustment is ∞ (infinity).
(ii) Final Image Formed at the Least Distance of Distinct Vision (25cm):
In this case, the final image is formed at the least distance of distinct vision (25cm). Therefore, the objective lens angular magnification (M_o) = 1.
M_e (Eyepiece angular magnification) can be calculated using the same formula as before:
M_e = 1 + (D_f / D_o)
Where:
D_f is the final image distance formed by the objective lens (25cm).
D_o is the distance of distinct vision (25cm).
M_e = 1 + (25 / 25) = 1 + 1 = 2
Angular magnification (M) = M_o * M_e = 1 * 2 = 2
Therefore, the angular magnification of the telescope when the final image is formed at the least distance of distinct vision (25cm) is 2.