1.

The semi vertical angle of the cone of the rays incident on the objective of a microscope is 20°. If the wavelength of incident light is 6600 Å, calculate the smallest distance between two points which can be just resolved.

Answer»

Data : α = 20°, 

λ = 6600 Å = 6.6 × 10-7 m, 

n = 1 (air) resolution between two closely-spaced distant objects so that they are just resolved when seen through the telescope. 

Formula : Resolving power of a telescope

R = \(\cfrac 1θ\) = \(\cfrac D{1.22λ}\)

where θ ≡ the minimum angular separation of two closely-spaced celestial objects or the angular limit of resolution, D ≡ the diameter of the objective lens of the telescope, λ ≡ the wave length of light.

Advantages of a large objective lens in an astronomical telescope :

1. The resolving power is directly proportional to the diameter of the objective lens. Hence, a large objective lens results in a smaller Airy disc and a sharper image. 

2. It collects more of the incident radiation from a distant object which results in a brighter image.



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