Match List - I with List - II.
| List-I | List-II |
| (A) Resolving power of an astronomical telescope | (I) \( 1.22\lambda/D \) |
| (B) Limit of resolution of an astronomical telescope | (II) \( \mu\sin\theta \) |
| (C) Numerical aperture | (III) \( D/1.22\lambda \) |
| (D) Fresnel distance | (IV) \( a^{2}\lambda^{-1} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (III), (B) - (I), (C) - (II), (D) - (IV)
Diffraction at the aperture of an optical instrument limits how close two objects can be and still be seen as separate.
(A) Resolving power of an astronomical telescope — this matches (III) \( D/1.22\lambda \). The resolving power is the reciprocal of the smallest angle the telescope can resolve, so it increases with the aperture \( D \) of the objective.
(B) Limit of resolution of an astronomical telescope — this matches (I) \( 1.22\lambda/D \). The limit of resolution is the smallest angular separation of two stars that can be seen as separate.
(C) Numerical aperture — this matches (II) \( \mu\sin\theta \). For a microscope objective, the refractive index \( \mu \) of the medium between object and objective times the sine of the half-angle of the cone of light accepted is called the numerical aperture.
(D) Fresnel distance — this matches (IV) \( a^{2}\lambda^{-1} \). The Fresnel distance \( z_F = a^{2}/\lambda \) is the distance a beam of width \( a \) travels before diffraction spreading becomes significant.