Tag: diffraction

Quizzes (0) Questions (157)

Questions Related to diffraction

Multiple choice physics wave optics resolving power of optical instruments resolution of optical instruments diffraction

An astronomical telescope has a large aperture to

  1. reduce spherical aberration

  2. have high resolution

  3. increase span of observation

  4. have low dispersion
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The aperture of an astronomical telescope is defined as the diameter of the objective lens.
In telescopes since, the stars are very far away from away us and emit light internsities, we need a large aperture to increase the amount of light entering the telescope thereby increasing the resolution

Multiple choice physics wave optics resolving power of optical instruments resolution of optical instruments diffraction

The limit of resolution of an optical instrument is the smallest angle that two points on an object have to subtend at the eye so that they are.

  1. Unresolved

  2. Well resolved

  3. Just resolved

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Limit of resolution of an optical instrument is the minimum angle that two points on an object have to subtend at the eye so that they are just resolved. (C)

Multiple choice physics wave optics resolving power of optical instruments resolution of optical instruments diffraction

To increase the magnification of a telescope 

  1. the objective lens should be of large focal length and eyepiece should be of small focal length.

  2. the objective and eyepiece both should be of large focal length.

  3. both the objective and eyepiece should be of smaller focal lengths

  4. the objective should be of small focal length and eyepiece should be of large focal length
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$m=\dfrac { { f } _{ o } }{ { f } _{ e } } $
from the above relation we can see that magnification is directly proportional to the focal length of objective lens.
Multiple choice physics wave optics resolving power of optical instruments resolution of optical instruments diffraction

Magnification of an object ($m$), is equal to

  1. $\cfrac {v+f}{f}$
  2. $\cfrac {vf}{v-f}$
  3. $\cfrac {f}{v+f}$

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

we know,mirror formula
$\cfrac {1}{f}=\cfrac{1}{v}+\cfrac{1}{u}, magnification(m)=\cfrac{-v}{u}$
$\cfrac{1}{u}=\cfrac{1}{f}-\cfrac{1}{v}$
$\cfrac{1}{u}=\cfrac{v-f}{fv}$
${u}=\cfrac{fv}{v-f}$
$(m)=\cfrac{-v}{u}$,substituting $u$.
$m=\cfrac{-v}{1}\times\cfrac{v-f}{fv}$
$m=\cfrac{f-v}{f}$

Multiple choice physics wave optics resolving power of optical instruments resolution of optical instruments diffraction

Calculate the limit of resolution of a telescope objective having a diameter of 200 cm, if it has to detect light of wavelength 500 nm coming from a star ; -

  1. $305 \times 10^{-9} $ radian
  2. $152.5 \times 10^{-9} $ radian
  3. $610 \times 10^{-9} $ radian
  4. $457.5 \times 10^{-9} $ radian
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Limit of resolution of telescope = $\dfrac{1.22 \lambda}{D}$
$\theta = \dfrac{1.22 \times 500 \times 10^{-9}}{200 \times 10^{-2}} = 305 \times 10^{-9}$ radian

Multiple choice physics wave optics resolving power of optical instruments resolution of optical instruments diffraction

In an electron microscope the accelerating voltage is increased from 20 kV to 80 kV, the resolving power of the microscope will change from R to

  1. $2 R$
  2. $\dfrac{R}{2}$
  3. $4R$
  4. $3R$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Electron microscope is a microscope that can magnify very small details with high resolving power due to the use of electrons as the source of illumination. Since the wavelength of electrons are 100,000 times shorter than visible light the electron microscopes have greater resolving power
We have the Abbe's formula as resolution limit $d=\dfrac{0.61\lambda}{NA}$(NA is the numerical aperture)


The resolving power increases when d, the minimum distance that can be seen between two points in the image, decreases. Thus, according to the formula the resolving power is inversely proportional to the wavelength.

Resolving Power  $\propto \dfrac{1}{\lambda}$

A higher voltage will give the electrons a higher speed. Thus the electrons will have a smaller de Broglie wavelength according to the equation,  $\lambda=h/mv$

$\lambda\propto\dfrac{1}{\sqrt V}$

Thus we get Resolving power $\propto \sqrt{V}$

$ \implies\dfrac{R}{R'} = \sqrt{\dfrac{20}{80}} $

Thus, $R' = 2R$

Multiple choice physics wave optics resolving power of optical instruments resolution of optical instruments diffraction

An astronomical telescope, consists of two thin lenses set $36 cm$ a part and has a magnifying power $8$. Calculate the focal length of the lenses.

  1. $32 cm$
  2. $18 cm$
  3. $25 cm$
  4. $36 cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Here, $f _o+f _e=36 cm$
$M=-8$ (magnifying power is negative)
Now, $M=\cfrac {f _o}{f _e}$
$\therefore -8=-8=-\cfrac {f _o}{f _e}$
$\Rightarrow f _o=8f _e$

From the equations, we have
$8f _e+f _e=36$ or $f _e=4\ cm$

Again, $f _o=8f _e=8\times 4=32\ cm$