A simple telescope used to view distant object has eyepiece...

A simple telescope used to view distant object has eyepiece and objective lenses of focal lengths $f_{e}$ and $f_{01}$ respectively. Then Column I Column II $L$ intensity of light received (A) Radius of aperture by lens II Angular magnification (B) Dispersion of lens Iil. Length of telescope (C) Focal length of objective lens and eyepiece lens IV. Sharpness of image (D) Spherical aberration Code (a) $1-\mathrm{A} ; \|-\mathrm{C} ; 111-\mathrm{C} ; \mathrm{I}-\mathrm{A}, \vec{B} ; \mathrm{C}$ (b) $\mid-\mathrm{A} ; \mathrm{ll}-\mathrm{B} ; \mathrm{III}-\mathrm{C}_{i} \mathrm{~N}-\mathrm{D}$ (c) $1-\mathrm{D} ; \mathrm{II}-\mathrm{B} ; \mathrm{C} ; \| 1-\mathrm{A} ; \mathrm{IV}-\mathrm{C} ; \mathrm{D}$ (d) $1-\mathrm{C}, \mathrm{D} ; \|-\mathrm{B} ; \mathrm{C} ; \mathrm{D} ; \mathrm{II}-\mathrm{A} ; \mathrm{B} ; \mathrm{IV}-\mathrm{A}$

A simple telescope used to view distant object has eyepiece and objective lenses of focal lengths $f_{e}$ and $f_{01}$ respectively. Then Column I Column II
$L$ intensity of light received
(A) Radius of aperture by lens
II Angular magnification
(B) Dispersion of lens
Iil. Length of telescope
(C) Focal length of objective lens and eyepiece lens
IV. Sharpness of image
(D) Spherical aberration Code
(a) $1-\mathrm{A} ; \|-\mathrm{C} ; 111-\mathrm{C} ; \mathrm{I}-\mathrm{A}, \vec{B} ; \mathrm{C}$
(b) $\mid-\mathrm{A} ; \mathrm{ll}-\mathrm{B} ; \mathrm{III}-\mathrm{C}_{i} \mathrm{~N}-\mathrm{D}$
(c) $1-\mathrm{D} ; \mathrm{II}-\mathrm{B} ; \mathrm{C} ; \| 1-\mathrm{A} ; \mathrm{IV}-\mathrm{C} ; \mathrm{D}$
(d) $1-\mathrm{C}, \mathrm{D} ; \|-\mathrm{B} ; \mathrm{C} ; \mathrm{D} ; \mathrm{II}-\mathrm{A} ; \mathrm{B} ; \mathrm{IV}-\mathrm{A}$

Key Concepts

Angular Magnification

In optical instruments, angular magnification refers to the ratio by which a telescope increases the apparent angular size of an object. It is determined by the focal lengths of the objective and eyepiece lenses, and it essentially quantifies how much larger a distant object appears when viewed through the instrument.

Focal Length of Lenses

The focal length of a lens is the distance from the lens at which parallel rays of light converge to a point. In telescopes, the objective lens’s focal length primarily determines the image formation, while the combination of the objective and eyepiece focal lengths is crucial in setting the overall magnification and performance of the telescope.

Aperture and Light Collection

The aperture of a telescope, specifically the radius of the objective lens, plays a key role in determining the intensity of light received. A larger aperture allows more light to enter, which is essential for viewing faint and distant objects by improving both resolution and brightness.

Dispersion in Lenses

Dispersion is the phenomenon where a lens separates light into its constituent wavelengths, leading to chromatic aberration. This effect can cause different colors of light to focus at different points, thereby degrading the quality of the image if not corrected.

Spherical Aberration

Spherical aberration is an optical effect found in lenses where rays that strike the lens near its edge do not converge at the same point as those that strike near the center. This aberration results in a blurred or imperfect image, affecting the sharpness and overall quality of the imaging system.

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