Question 74: Ray Optics

Question

A simple telescope used to view distant objects has eyepiece and objective lens of focal lengths $f_e$ and $f_0$, respectively. Match Column I with Column II:

Column I
Column II

(A)
Intensity of light received by lens.
(P)
Radius of aperture(R).

(B)
Angular magnification.
(Q)
Dispersion of lens.

(C)
Length of telescope.
(R)
Focal length $f_0, f_e$.

(D)
Sharpness of image.
(S)
Spherical aberration.

Accepted Answer

(A) Intensity of light received by the lens
The amount of light collected (intensity received) depends on the
aperture (radius R)
of the objective lens.
Larger radius Ã¢ÂÂ more light collected Ã¢ÂÂ brighter image.
Ã¢ÂÂ
(A) Ã¢ÂÂ (P)
.
(B) Angular magnification
For a simple telescope (in normal adjustment),
$   M = \frac{f_0}{f_e}.   $
So, magnification depends on
focal lengths $f_0, f_e$
.
Ã¢ÂÂ
(B) Ã¢ÂÂ (R)
.
(C) Length of telescope
Optical length of telescope in normal adjustment is
$   L = f_0 + f_e.   $
Again depends on
focal lengths $f_0, f_e$
.
Ã¢ÂÂ
(C) Ã¢ÂÂ (R)
.
(D) Sharpness of image
Sharpness (freedom from blurring) is affected by optical
aberrations
:
Spherical aberration (S)
: due to large aperture.
Chromatic aberration / dispersion (Q)
: due to different focal lengths for different colors.
Both dispersion and spherical aberration degrade sharpness.
Ã¢ÂÂ
(D) Ã¢ÂÂ (P, Q, S)
Ã¢ÂÂ P indirectly since aperture radius affects spherical aberration, but specifically aberrations (Q, S).
However, letÃ¢ÂÂs check options carefully:
Comparing to given options:
|
A
| D Ã¢ÂÂ (P, Q) (missing S) |
|
B
| D Ã¢ÂÂ (P, Q, S) Ã¢ÂÂ |
|
C
| Wrong A and C mappings |
|
D
| Wrong C, D mappings |
Ã¢ÂÂ
Correct option is Option B
$ \boxed{[\mathrm{A}	o(\mathrm{P}); \; \mathrm{B}	o(\mathrm{R}); \; \mathrm{C}	o(\mathrm{R}); \; \mathrm{D}	o(\mathrm{P},\mathrm{Q},\mathrm{S})]}  $

Answer

$$ [\mathrm{A} \rightarrow(\mathrm{P}) ; \mathrm{B} \rightarrow(\mathrm{R}) ; \mathrm{C} \rightarrow(\mathrm{R}) ; \mathrm{D} \rightarrow(\mathrm{P}, \mathrm{Q})]$$

Answer

$$ [\mathrm{A} \rightarrow(\mathrm{P}) ; \mathrm{B} \rightarrow(\mathrm{R}) ; \mathrm{C} \rightarrow(\mathrm{R}) ; \mathrm{D} \rightarrow(\mathrm{P}, \mathrm{Q}, \mathrm{~S})]$$

Answer

$$ [\mathrm{A} \rightarrow(\mathrm{R}) ; \mathrm{B} \rightarrow(\mathrm{P}) ; \mathrm{C} \rightarrow(\mathrm{R}) ; \mathrm{D} \rightarrow( \mathrm{Q}, \mathrm{~S})]$$

Answer

$$ [\mathrm{A} \rightarrow(\mathrm{P}) ; \mathrm{B} \rightarrow(\mathrm{R}) ; \mathrm{C} \rightarrow(\mathrm{S}) ; \mathrm{D} \rightarrow( \mathrm{Q})]$$

Ray Optics

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