Tag: wave optics

Questions Related to wave optics

Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wave length of light =500 nm]

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

  1. 10 m

  2. 5 m

  3. 15 m

  4. None of these

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Correct Option: B
Explanation:

We have, $\dfrac{y}{D}\ge 1.22 \dfrac{\lambda}{d}$


$\Rightarrow D \le \dfrac{yd}{(1.22)\lambda} = \dfrac{10^{-3}\times 3\times 10^{-3}}{(1.22)\times 5\times 10^{-7}}$

$=\dfrac{30}{6.1}\approx 5m$

$\therefore  D _{max} = 5m$

doctor prescribes spectacles to a patient with a combination of a convex lens of focal length 40 em, and concave lens of focal length 25 em then the power of spectacles will be.

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

  1. -6.5 D

  2. 1.5 D

  3. -1.5 D

  4. -8.5 D

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Correct Option: C
Explanation:

For combination of lenses, power
$P=P _1+P _2=\frac {100}{40}-\frac{100}{25}=-1.5 D$

An astronaut is looking down on earth's surface from a space shuttle an altitude of 400 km Assuming that the astronaut's pupil diameter is 5 mm and the wavelength of visible light is 500 nm, the astronaut will be able to resolve linear objects of the size of about :

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

  1. 0.5m

  2. 5m

  3. 50m

  4. 500m

Show answer
Correct Option: C
Explanation:

The resolving power of an instrument is given by the formula, $R.P=1.22\times \frac{\lambda D}{d}$
Here, d is aperture of the instruments, D is distance of satellite from the earth. Here eye is the optical instruments.
$\displaystyle R.P=\frac{1.22\times 500\times 10^{-9}}{5\times 10^{-3}}\times 400\times 1000$
          $\displaystyle =1.22\times \frac{10^{-2}}{10^{-3}}\times 4 = 1.22\times 40=50 m$

Assertion: The resolving power of a telescope is more if the diameter of the objective lens is more.
Reason: Objective lens of large diameter collects more light.

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

  1. Both assertion and reason are true but the reason is the correct explanation of assertion

  2. Both assertion and reason are true but the reason is not the correct explanation of assertion

  3. Assertion is true but reason is false

  4. Both the assertion and reason are false

  5. Reason is true but assertion is false

Show answer
Correct Option: A
Explanation:

The resolving power of a telescope increases as diameter of objective lens increases.
Resolving Power =D1.22λD1.22λ
where D is diameter of objective and λλ is wavelength of light used.

High quality lens system for optical instrument is made by using ..............

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

  1. Concave and convex lens

  2. Convex lens

  3. Concave lens

  4. Concave and convex mirror

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Correct Option: A

The limit of resolution of microscope, if the numerical aperture of microscope is 0.12, and the wavelength of light used is 600 nm, is 

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

  1. 0.3$\mu $m

  2. 1.2 $\mu $m

  3. 2.5$\mu $m

  4. 3$\mu $m

Show answer
Correct Option: C
Explanation:

For a microscope, the limit of resolution is given by,
 $X =  \dfrac{\lambda}{2A} $
where $ \lambda $ is the wavelength of light used, and A is the numerical aperture.
Hence, substituting the values,  $X =  \dfrac{600}{2 \times 0.12} $,
which gives, $X= 2.5  \mu m $

The optical instrument which is used in every cricket match is.:

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

  1. Simple microscope

  2. Compound microscope

  3. Astronomical telescope

  4. Binocular

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Correct Option: D
Explanation:

Binocular is used in every cricket match for the purpose of zooming.
Because, binoculars are a pair of mirror symmetrical telescopes that allow a user to view distant objects using both eyes. To allow both eyes to view distant objects symmetrically, the binoculars require two separate telescopes, one for each eye, held together in the device called binoculars allowing binocular vision. The telescopes are mounted symmetrically side-by-side and aligned to point accurately in the same direction, providing the user with undistorted vision of distant objects. Unlike a monocular (telescope) which only makes use of one telescope to view objects, binoculars are able to provide the user with three-dimensional viewing of distant objects, whilst promoting visual clarity and acuity.

A person wants to see two pillars from a distance of 11 km, separately. The distance between the pillars must be approximately

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

  1. 3.2m

  2. 1m

  3. 0.25 m

  4. 0.5 m

Show answer
Correct Option: A
Explanation:

Resolving power of eye = $ 1' = \dfrac {\pi} {60 \times 180} radians$ (approximately)


Let the separation between pillars $= x m$
Distance $= 11000 m$

=> $\dfrac {x} {11000} = \dfrac {\pi}{60 \times 180}$

=> $ x = 3.2 m$ (approximately)

Answer. A)$ 3.2m $

A telescope has an objective lens of 10 cm diameter and is situated at a distance of $1km$ for two objects. The minimum distance between these two objects, which can be resolved by the telesope, when the mean wavelength of light is 5000Å is of the order of

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

  1. 5 cm

  2. 0.5 mm

  3. 5 m

  4. 5 mm

Show answer
Correct Option: D
Explanation:

Resolution power $= \dfrac {d\lambda}{D} = \dfrac {1000 \times 5000 \times 10^{-10}}{10 \times 10^{-2}} = 5mm$

An astronomical telescope has a large aperture to

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

  1. reduce spherical aberration

  2. have high resolution

  3. increase span of observation

  4. have low dispersion

Show answer
Correct Option: B
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