nvppfThe following question appeared in MPPMT 2000 question paper:
The diameter of the objective of a telescope is ‘a’, its magnifying power is ‘m’ and the wave length of light is λ. The resolving power of the telescope is
(a) a/1.22 λ (b) λm/1.22a (c) 1.22a/ λ (d) a/1.22 λm
The magnifying power given in the problem is just a distraction. The limit of resolution of a telescope, which is the minimum angular separation between two objects that can be resolved is given by dθ = 1.22λ/a. The resolving power is the reciprocal of the limit of resolution and is equal to a/1.22 λ. [Option (a)].
Objectives and eye pieces of telescopes are made of achromatic combination of lenses to make them devoid of the defect of chromatic aberration. Consider the following MCQ:
A telescope objective is an achromatic doublet made of crown glass and flint glass lenses. The proper choice for the achromatic combination is
(a) divergent lens of flint glass and convergent lens of crown glass
(b) convergent lens of flint glass and divergent lens of crown glass
(c) both convergent (d) both divergent
(e) as given in options (a) or (b) or (c)
You might be remembering the condition for an achromatic doublet: ω1 /f1+ ω2/f2 = 0, from which ω1/f1= – ω2/f2.
Since the dispersive power ‘ω’ is a positive quantity, the negative sign shows that one lens must be diverging (negative focal length) and the other converging. In a telescope, the objective has to be converging. Therefore, the converging lens should have smaller focal length (larger power) so that when combined with the diverging lens, the combination will still be converging. Crown glass has smaller dispersive power and hence the converging lens should be made of crown glass to satisfy the above condition of achromatism [Option (a)].
The diameter of the objective of a telescope is ‘a’, its magnifying power is ‘m’ and the wave length of light is λ. The resolving power of the telescope is
(a) a/1.22 λ (b) λm/1.22a (c) 1.22a/ λ (d) a/1.22 λm
The magnifying power given in the problem is just a distraction. The limit of resolution of a telescope, which is the minimum angular separation between two objects that can be resolved is given by dθ = 1.22λ/a. The resolving power is the reciprocal of the limit of resolution and is equal to a/1.22 λ. [Option (a)].
Objectives and eye pieces of telescopes are made of achromatic combination of lenses to make them devoid of the defect of chromatic aberration. Consider the following MCQ:
A telescope objective is an achromatic doublet made of crown glass and flint glass lenses. The proper choice for the achromatic combination is
(a) divergent lens of flint glass and convergent lens of crown glass
(b) convergent lens of flint glass and divergent lens of crown glass
(c) both convergent (d) both divergent
(e) as given in options (a) or (b) or (c)
You might be remembering the condition for an achromatic doublet: ω1 /f1+ ω2/f2 = 0, from which ω1/f1= – ω2/f2.
Since the dispersive power ‘ω’ is a positive quantity, the negative sign shows that one lens must be diverging (negative focal length) and the other converging. In a telescope, the objective has to be converging. Therefore, the converging lens should have smaller focal length (larger power) so that when combined with the diverging lens, the combination will still be converging. Crown glass has smaller dispersive power and hence the converging lens should be made of crown glass to satisfy the above condition of achromatism [Option (a)].
You will find more multiple choice questions (with solution) on telescopes, microscopes and the defects of the eye at physicsplus: Questions on Optical Instruments
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