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Optical instruments : telescope - class-IX

Description: optical instruments : telescope
Number of Questions: 25
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Tags: option c: imaging physics ray optics and optical instruments optics observing space: telescopes
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A reflecting telescope has a large mirror for its objective with radius of curvature equal to 80 cm. The magnifying power of this telescope if eye piece used has a focal length of 1.6 cm is:

  1. 100

  2. 50

  3. 25

  4. 5


Correct Option: C
Explanation:

The focal length of objective mirror $f _0 = \dfrac{R}{2} = \dfrac{80}{2} = 40 \,cm$
and focal length of eye piece = 1.6 cm
$\therefore $ magnifying power, $m = \dfrac{f _0}{f _e} = \dfrac{40}{1.6 } = 25$

A telescope is used to resolve two stars separated by $4.6 \, \times \, 10^{-6}$ rad. If the wavelength of light used is 5460 $\overset{0}{A}$, what should be the aperture of the objective of the telescope? 

  1. 0.1488 m

  2. 0.567 m

  3. 1 m

  4. 2 m


Correct Option: A
Explanation:

Aperature of the telescope, $D = \dfrac{1.22\lambda}{d\theta}$ 


Here, $\lambda = 5460\ \overset{0}{A} = 5460 \times 10^{-10}m$


$ d\theta= 4.6 \times10^{-6}\ rad$

$\therefore D = \dfrac{1.22\times5460\times10^{-10}}{4.6\times 10^{-6}}$
$ = 0.1488m $

If you want to make Refracting Telescope, what components will you choose ?

  1. One convex led and one concave lens.

  2. Two convex lenses.

  3. One concave mirror, one plane mirror and one convex lens.

  4. Once concave mirror, one convex mirror and one convex lens.


Correct Option: B
Which material should be chosen to make the concave mirrors of a high resolution telescope so that it can also withstand temperature variations?
  1. Quartz

  2. Flint glass

  3. Crown glass

  4. Combination of Flint and Silica


Correct Option: A
Explanation:

Quartz makes an ideal mirror. Its high hardness results in the smoothest micropolished surface possible, and its thermal dimensional stability allows the optician to produce a flat surface with almost no edge defects.

Scientists identify the elements that are burning in the stars by using which of the following devices?

  1. Refractive telescopes

  2. Reflective telescopes

  3. Spectroscopes

  4. Polarimeters

  5. Photoelectric mircoscopes


Correct Option: C
Explanation:
Using the spectroscope, scientists can separate the individual line spectra of the elements that are burning in the stars and therefore identify the elements.

Two convex lenses of focal length 0.3 m and 0.05 m are used to make a telescope. The distance kept between them is equal to 

  1. 0.35 m

  2. 0.25 m

  3. 0.175 m

  4. 0.15 m


Correct Option: A
Explanation:

To make a Telescope,
$L= f _{0}+f _{e}$

$= 0.3+0.05$

$= 0.35m$

In an astronomical telescope of refracting type:

  1. Eyepiece has greater focal length

  2. Objective has greater focal length

  3. Objective and eyepiece have equal focal length

  4. Eyepiece has greater aperture than the objective


Correct Option: B
Explanation:

An astronomical telescope of refracting type has objective of greater focal length to have more surface area for incoming light from celestial bodies. 

Four lenses of focal length $+15cm,+20cm,+150cm$ and $+250cm$ are available for making an astronomical telescope. To produce the largest magnification, the focal length of the eyepiece should be

  1. $+15cm$

  2. $+20cm$

  3. $+150cm$

  4. $+250cm$


Correct Option: A
Explanation:

In astronomical telescope, magnification is inversely proportional to focal length of eye piece. Hence, it will be minimum i.e. +15cm as in question.

A reflecting telescope utilises :

  1. a convex mirror

  2. a concave mirror

  3. a prism

  4. a plano-concave lens


Correct Option: B
Explanation:

Unlike convex mirrors, concave mirrors show different image types depending on the distance between the object and the mirror. That is why a reflecting telescope utilizes a concave mirror. If you observe the design of a reflecting telescope, it uses the incoming rays to focus through a concave mirror to focus on the second mirror which in turn sends the rays to the eye-piece. So, the concave mirror is intrinsic to the design of a reflecting telescope.

This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1 : Very large size telescopes are reflecting telescopes instead of refracting telescopes.
Statement 2 : It is easier to provide mechanical support to large size mirrors than large size lenses.

  1. Statement-1 is true and Statement-1 is false and statement-2 is true

  2. Statement-1 is false and Statement-2 is true

  3. Statements-1 and Statement-2 are true and Statement-2 is correct explanation for Statement-1

  4. Statements-1 and Statements-2 are true and Statement-2 is not the correct explanation for Statement-1


Correct Option: C

In the spectrum of light from a star, the wavelength of a particular line is measured to be $4747 $, while the actual wavelength of the line is $4700 $. What is the relative velocity ?

  1. $2\times10^5 m/s$

  2. $3\times10^5 m/s$

  3. $3\times10^6 m/s$

  4. $4.5\times10^6 m/s$


Correct Option: B

The objective of a telescope A has diameter 3 times that of the objective of telescope B, How much greater amount of light is gathered by A as compared to B?

  1. $\dfrac { 1 }{ 9 } $

  2. $\dfrac { 1 }{ 3 } $

  3. 3

  4. 9


Correct Option: A

In telescope, ratio of resolving power due to light of $\lambda=400\mathring {A}$ and $\lambda =6000\mathring {A}$ is ______

  1. $4:5$

  2. $3:2$

  3. $2:3$

  4. $5:4$


Correct Option: B

For an electron microscope, which of the following is false ?

  1. It uses magnetic lens to converge electron beam.

  2. Its resolving power is directly proportional to accelerating potential of electron.

  3. Its resolving power is inversely proportional to wavelength of electrons

  4. Magnification attained with the help of of it of the order of $10^6$.


Correct Option: B

 If an object subtend angle of $2^o$ at eye when seen through telescope having objective and eyepiece of focal length $f = 60\, cm $and $f = 5\, cm$ respectively than angle subtend by image at eye piece will be 

  1. $16^o$

  2. $50^o$

  3. $10^o$

  4. $24^o$


Correct Option: A

A telescope has an objective of focal length $50 cm$ and an eye-piece of focal length $5 m$ THe least distance of distinct vision is $25 cm$. The telescope is focused for distinct vission a scale $200 cm$ away from the objective.The separation between the two lenses is nearly 

  1. $71 cm$

  2. $61 cm$

  3. $81 cm$

  4. $51 cm$


Correct Option: A

Match the items given in A, B, C and D against their corresponding description given in 1, 2, 3, 4 and 5.
A. Astronomical telescope
B. Galilean Telescope
C. Simple Microscope
D. Compound Microscope

1. Contains one convex lens
2. Contains one concave lens
3. Contains a convex lens of large focal length in the objective and a convex lens of small focal length in the eye-piece
4. Contains a convex lens of small focal length in the objective and a convex lens of large focal length in the eye-piece
5. Contains a convex lens of large focal length in the objective and a concave lens of small focal length in the eye-piece. 

  1. $2\, \quad\, 3\, \quad\, 1\, \quad\, 5$

  2. $3\, \quad\, 2\, \quad\, 4\, \quad\, 1$

  3. $2\, \quad\, 5\, \quad\, 3\, \quad\, 4$

  4. $3\, \quad\, 5\, \quad\, 1\, \quad\, 4$


Correct Option: D
Explanation:

A). Astronomical telescope - Contains a convex lens of large focal length in the objective and a convex lens of small focal length in the eye-piece

B.) Galilean Telescope - Contains a convex lens of large focal length in the objective and a concave lens of small focal length in the eye-piece
C). Simple Microscope - Contains one convex lens
D.) Compound Microscope - Contains a convex lens of small focal length in the objective and a convex lens of large focal length in the eye-piece
Thus,
A  -  3 , B  -  5 , C  -  1 and D  -  4 , hence Option D is correct.

The sum of the focal lengths of the objective and an eyepiece, In case of an astronomical telescope is equal to : ( final image is at $\infty$)

  1. The length of the telescope

  2. Half the length of the telescope

  3. Double the length of the telescope

  4. None of these


Correct Option: A
Explanation:

Answer is A.

The astronomical telescope makes use of two positive lenses: the objective, which forms the image of a distant object at its focal length, and the eyepiece, which acts as a simple magnifier with which to view the image formed by the objective. Its length is equal to the sum of the focal lengths of the objective and eyepiece, and its angular magnification is -fo/fe , giving an inverted image.
Hence, the sum of the focal lengths of the objective and an eyepiece, In case of an astronomical telescope is equal to the length of the telescope.

By which instrument we collect the space information:

  1. Convex lens

  2. Microscope

  3. Hubble Telescope

  4. None of these


Correct Option: C
Explanation:

Hubble Telescope is a device used to collect space information.

The focal lengths of the objective and the eyepiece of an astronomical telescope are 20 cm and 5 cm respectively. If the final image is formed at a distance of 30 cm from the eyepiece, find the separation between the lenses required for distinct vision

  1. 32.4 cm

  2. 42.3 cm

  3. 24.3 cm

  4. 30.24 cm


Correct Option: C
Explanation:

$f _{0}=20cm$


$f _{e}=5cm$

$V _{e}=30cm = D$

$L=?$

$L _{D}=f _{0}+ \dfrac{Df _e}{D+f _e}$ $=20+\dfrac{5\times 30}{35}=24.3 cm$

The focal length of the objective of an astronomical telescope is 1 m and it is in normal adjustment.Initially the telescope is focussed to a heavenly body. If the same telescope is to be focussed to an object at a distance of 21 m from the objective,then identify the correct choice

  1. eye piece should be displaced by 2 cm away from the objective

  2. eye piece should be displaced by 2 cm towards the objective

  3. eye piece should be displaced by 5 cm towards the objective

  4. eye piece should be displaced by 5 cm away from the objective


Correct Option: D
Explanation:

We know, $ \dfrac {1}{f} = \dfrac {1}{v} - \dfrac {1} {u} $


We seeing heavenly body,  $u =  \infty$
$v = f = 1 m$

When seeing 21 m far
$u = - 21 m $
$f = 1 m$
$v = \dfrac {f u} {(f+u)} = 21 / 20 = 1.05 m$

So, eye piece need to move $1.05-1 = 0.05 m$ further away from objective

Answer. D) eye piece should be displaced by $5 cm$ away from the objective

The focal lengths of the objective and eyepiece of a telescope are 60cm and 5cm respectively.The telescope is focused on an object 360cm from the objective and the final image is formed at a distance of 30cm from the eye of the observer. The length of the telescope is

  1. 66.3 cm

  2. 86.3 cm

  3. 76.3 cm

  4. 96.3 cm


Correct Option: C
Explanation:

$f _o = 60cm$


$f _e = 5cm$

$r _e = 30cm$

$L = ?$

$u _o = 360cm$

$\dfrac {1}{v _o} + \dfrac {1}{360} = \dfrac {-1}{60}$

$\dfrac {1}{v _o} = \dfrac {-1}{60} + \dfrac {1}{360}$

In which of the following instruments is the final image virtual?

  1. Projector

  2. Camera

  3. Microscope

  4. Telescope


Correct Option: C,D
Explanation:

The final image of the camera and projector is real because it is obtained or projected on a screen or a photographic film or a chip.

A simple microscope uses convex lens and the object is placed between the focus and the optical center, so that, an erect, virtual and enlarged image of the object is formed.

A telescope uses two co-axially placed convex lenses in such a way that the focus of objective lens is past the focus of the eye piece. The first lens or the objective lens produces a real and inverted image of the object to be observed and this real image formed acts as an object for the eye piece convex lens and is between the focus and the optical center, so that, an inverted, virtual and enlarged image of the object is formed.

Hence, the correct answers are OPTIONS C and D.  

A planet is observed by an astronomical reflecting telescope having an objective of focal length $16 m$ and an eye-piece of focal length $2 cm$. Then :

  1. the distance between the objective and the eye - piece is $16.02 m$

  2. the angular magnification of the planet is $800$

  3. the image of planet is erect

  4. the objective is larger than eye - piece


Correct Option: A,B,D
Explanation:

A telescope uses two co-axially placed convex lenses in such a way that the focus of objective lens is past the focus of the eye piece as evident here from the focal lengths of the objective lens and the eye piece. $ \therefore $ The objective lens is larger than eye piece.

Length of the tube is given as 
$ L = f _o + f _e = 16\ m + 2\ cm = 16.02\ m $

Angular magnification is given as:
$ m = \dfrac{f _o}{f _e} = \dfrac{1600}{2} = 800 $


Since, the first lens or the objective lens produces a real and inverted image of the object to be observed and this real image formed acts as an object for the eye piece convex lens and is between the focus and the optical center, so, an inverted, virtual and enlarged image of the object is formed. $ \therefore $ The final image is inverted. 

Hence, the correct answers are OPTIONS A,B and D.

An astronomical refracting telescope will have large angular magnification and high angular resolution, when it has an objective lens of

  1. large focal length and small diameter

  2. large focal length and large diameter

  3. small focal length and large diameter

  4. small focal length and small diameter


Correct Option: B
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