Optical Instruments

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The focal lengths of the objective and the eyepiece of a compound microscope are 2.0 cm and 3.0 cm respectively. The distance between the objective and the eyepiece is 15.0 cm. The final image formed by the eyepiece is at infinity. The two lenses are thin. The distance in cm of the object and the image produced by the objective, measured from the objective lens, are respectively

The resolving power of electron microscope is higher than that of an optical microscope because the wavelength of electrons is …… than the wavelength of visible light.

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A planet is observed by an astronomical refracting telescope having an objective of focal length $16 m$ and an eyepiece of focal length $2 cm$

* Multiple Correct Options

(A)

the distance between the objective and the eyepiece is

16.02 m

(B)

the angular magnification of the planet is

- 800

(C)

the image of the planet is inverted

(D)

the objective is larger than the eyepiece

JEE Advanced 2006

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Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II.

List-I

(P)

Intensity of light received by lens

(Q)

Angular magnification

List-II

(1)

radius of aperture (

R

f_{o}, f_{e}

(4)

spherical aberration

LEVELJEE Main

An astronomical telescope has an angular magnification of magnitude $5$ for far objects. The separation between the objective and the eyepiece is $36 cm$ and the final image is formed at infinity. The focal length $f_{o}$ of the objective and the focal length $f_{e}$ of the eyepiece are

(A)

f_{o} = 45 cm

and

f_{e} = - 9 cm

(B)

f_{o} = 50 cm

and

f_{e} = 10 cm

(C)

f_{o} = 7.2 cm

and

f_{e} = 5 cm

(D)

f_{o} = 30 cm

and

f_{e} = 6 cm

LEVELJEE Main

An astronomical telescope has an angular magnification of magnitude $5$ for far objects. The separation between the objective and the eyepiece is $36 cm$ and the final image is formed at infinity. The focal length $f_{o}$ of the objective and the focal length $f_{e}$ of the eyepiece are

(A)

f_{o} = 45 cm

and

f_{e} = - 9 cm

(B)

f_{o} = 50 cm

and

f_{e} = 10 cm

(C)

f_{o} = 7.2 cm

and

f_{e} = 5 cm

(D)

f_{o} = 30 cm

and

f_{e} = 6 cm

JEE Main 2020

LEVELJEE Main

The aperture of a telescope is $5 m$ . The separation between the moon and the earth is $4 \times 1 0^{5} km$ . With light of wavelength of $5500 \overset{˚}{A}$ , the minimum separation between objects on the surface of moon, so that they are just resolved, is close to

(A)

600 m

(B)

20 m

(C)

60 m

(D)

200 m

JEE Main 2021

LEVELBoard

Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as non-uniform and distorted. The doctor diagnosed the problem as

(A)

astigmatism

(B)

myopia with astigmatism

(C)

presbyopia with astigmatism

(D)

myopia and hypermetropia

JEE Main 2020

LEVELJEE Main

If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eyepiece should be close to

An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification 6, gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length 0.6 m, if the focal length of the eyepiece is equal to ......... cm.

JEE Main 2015

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Assuming human pupil to have a radius of $0.25 cm$ and a comfortable viewing distance of $25 cm$ , the minimum separation between two objects that human eye can resolve at $500 nm$ wavelength is

(A)

1 μ m

(B)

30 μ m

(C)

100 μ m

(D)

300 μ m

JEE Main 2008

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An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment, distances are measured by

(A)

a vernier scale provided on the microscope

(B)

a standard laboratory scale

(C)

a meter scale provided on the microscope

(D)

a screw gauge provided on the microscope

JEE Main 2019

LEVELJEE Main

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.

(A)

610 \times 1 0^{- 9} rad

(B)

305 \times 1 0^{- 9} rad

(C)

457.5 \times 1 0^{- 9} rad

(D)

152.5 \times 1 0^{- 9} rad

JEE Main 2020

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In a compound microscope, the magnified virtual image is formed at a distance of 25 cm from the eye-piece. The focal length of its objective lens is 1 cm. If the magnification is 100 and the tube length of the microscope is 20 cm, then the focal length of the eye-piece lens (in cm) is ......... .

JEE Main 2019

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The value of numerical aperture of the objective lens of a microscope is $1.25$ . If light of wavelength $5000 \overset{˚}{A}$ is used, the minimum separation between two points, to be seen as distinct, will be

(A)

0.24 μ m

(B)

0.38 μ m

(C)

0.12 μ m

(D)

0.48 μ m

LEVELJEE Main

The image formed by an objective of a compound microscope is

(A)

virtual and diminished

Wavelength of light used in an optical instrument are $λ_{1} = 4000 \overset{˚}{A}$ and $λ_{2} = 5000 \overset{˚}{A}$ , then ratio of their respective resolving powers (corresponding to $λ_{1}$ and $λ_{2}$ ) is

An observer looks at a distance tree of height 10 m with a telescope of magnifying power of 20. To the observer the tree appears

A compound microscope consists of an objective lens of focal length $1$ cm and an eye piece of focal length $5$ cm with a separation of $10$ cm. The distance between an object and the objective lens, at which the strain on the eye is minimum is $\frac{n}{40}$ cm. The value of $n$ is …… .

JEE Main 2021

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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) For a simple microscope, the angular size of the object equals the angular size of the image. Reason (R) Magnification is achieved as the small object can be kept much closer to the eye than 25 cm and hence, it subtends a large angle. In the light of the above statements, choose the most appropriate answer from the options given below.

(A)

A is true but R is false.

(B)

Both A and R are true but R is not the correct explanation of A.

(C)

Both A and R are true and R is the correct explanation of A.

(D)

A is false but R is true.

JEE Main 2019

LEVELJEE Main

Diameter of the objective lens of a telescope is $250 cm$ . For light of wavelength $600 nm$ coming from a distant object, the limit of resolution of the telescope is close to

(A)

3.0 \times 1 0^{- 7} rad

(B)

2.0 \times 1 0^{- 7} rad

(C)

1.5 \times 1 0^{- 7} rad

(D)

4.5 \times 1 0^{- 7} rad

JEE Main 2020

LEVELJEE Main

The magnifying power of a telescope with tube length $60 cm$ is $5$ . What is the focal length of its eyepiece?

(A)

10 cm

(B)

20 cm

(C)

30 cm

(D)

40 cm

JEE Main 2002

LEVELJEE Main

An astronomical telescope has a large aperture to

(A)

reduce spherical aberration

(B)

have high resolution

(C)

increase span of observation

(D)

have low dispersion

LEVELJEE Main

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?\n[Take wavelength of light $= 500 nm$ ]

(A)

5 m

(B)

1 m

(C)

6 m

(D)

3 m

The resolving power of electron microscope is higher than that of an optical microscope because the wavelength of electrons is …… than the wavelength of visible light.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A planet is observed by an astronomical refracting telescope having an objective of focal length 16 m and an eyepiece of focal length 2 cm

Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II.

List-I

List-II

Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as non-uniform and distorted. The doctor diagnosed the problem as

If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eyepiece should be close to

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment, distances are measured by

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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.

In a compound microscope, the magnified virtual image is formed at a distance of 25 cm from the eye-piece. The focal length of its objective lens is 1 cm. If the magnification is 100 and the tube length of the microscope is 20 cm, then the focal length of the eye-piece lens (in cm) is ......... .

The image formed by an objective of a compound microscope is

An observer looks at a distance tree of height 10 m with a telescope of magnifying power of 20. To the observer the tree appears

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600 nm coming from a distant object, the limit of resolution of the telescope is close to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The magnifying power of a telescope with tube length 60 cm is 5. What is the focal length of its eyepiece?

An astronomical telescope has a large aperture to

A planet is observed by an astronomical refracting telescope having an objective of focal length $16 m$ and an eyepiece of focal length $2 cm$

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.

Diameter of the objective lens of a telescope is $250 cm$ . For light of wavelength $600 nm$ coming from a distant object, the limit of resolution of the telescope is close to

The magnifying power of a telescope with tube length $60 cm$ is $5$ . What is the focal length of its eyepiece?