Limit of Resolution

Q. Assuming that light of wavelength $6000\mathring{\text{A}}$ is coming from a star. What is the limit of resolution of a telescope whose objective has diameter of $122\text{cm}?$

1. $3\times {10}^{–7}\text{rad}$
2. $6\times {10}^{–7}\text{rad}$
3. $9\times {10}^{–7}\text{rad}$
4. $7\times {10}^{–7}\text{rad}$

Q. Electrons used in an electron microscope are accelerated through a voltage of $25\text{kV}$. If voltage is increased to $100\text{kV}$ then the de-Broglie wavelength associated with the electrons will

1. increased by $4$ times.
2. be doubled.
3. be halved.
4. decreased by $4$ times.

Q. Two point white dots are $1\text{mm}$ apart on a black paper. The are viewed by the eye of pupil diameter $3\text{mm}$. Approximately, the minimum distance(in $mt$ at which these dots can be resolved by the eye is
Take wavelength to be $500\text{nm}$

Q. A telescope has an objective lens of 10 cm diameter and is situated at a distance one kilometre from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is $5000\stackrel{\circ }{A}$, is of the order of

1. 0.5 m
2. 5 m
3. 5 mm
4. 5cm

Q.

A small telescope has an objective lens of focal length 150 cm and an eye-piece of focal length 5 cm. What is the magnifying power of the telescope for viewing distant objects in normal adjustment?
If this telescope is used to view a 100 m tall tower 3 km away, what is the height of the image of the tower formed by the objective lens?

Q.

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

1. 10 times nearer

2. 10 times taller

3. 20 times taller

4. 20 times nearer

Q. Two points separated by a distance of 0.1 mm can just be resolved by a microscope when light of wavelength $6000\stackrel{\circ }{A}$ is used. If light of wavelength 4800 Å is used, this limit of resolution becomes

1. 0.08 mm
2. 0.10 mm
3. 0.12 mm
4. 0.06 mm

Q.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: An electron microscope can achieve better resolving power than an optical microscope.

Reason R: The de Broglie’s wavelength of the electrons emitted from an electron gun is much less than the wavelength of visible light.

In light of the above statements, choose the correct answer from the options given below:

1. A is true but R is false.

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

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

4. A is false but R is true.

Q. To increase both the resolving power and magnifying power of a telescope

1. both the focal length and aperture of the objective have to be increased.
2. the focal length of the objective has to be increased.
3. the aperture of the objective has to be increased.
4. the wavelength of light has to be decreased.

Q. An object viewed from a near point distance of $25\text{cm}$, 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 $0.6\text{m}$, if the focal length of the eyepiece is equal to _____ $\text{cm}$.

Q. The resolution limit of eye is 1 minute. At a distance of r from the eye, two persons stand with a lateral separation of 3 metre. For the two persons to be just resolved by the naked eye, r should be

1. 10 km
2. 15 km
3. 30 km
   
4. 20 km

Q. An astronomical telescope consists of an objective of focal length 60 cm and an eye - piece of focal length 5 cm. It is focused on a distant object such that the rays emerging from the eye - lens are parallel. The object subtends an angle of $2^{\circ }$ at the objective. The angular width of the image is

1. ${54}^{\circ }$
2. ${10}^{\circ }$
3. ${24}^{\circ }$
4. ${48}^{\circ }$

Q. Position of the final image of an object $\text{O}$ (as shown in the figure) with respect to the plane surface will be

1. $14\text{cm}$ below
2. $14\text{cm}$ above
3. $21\text{cm}$ below
4. $21\text{cm}$ above

Q.

A person can see the objects lying between $25cm$ and the $10m$ from his eye. His vision can be corrected by using lens of power:

Q. A glass slab of referactive index $\mu =1.5$ and thickness of 15 cm is placed in front of a convex mirror as shown in figure.


The distance between the actual position of pole and image of object $O$ as seen by the observer will be:

1. $9\text{cm}$
2. $25\text{cm}$
3. $15\text{cm}$
4. $18\text{cm}$

Q.

The wavelength of maximum emitted energy of a body at 700 K is 4.08 $\mu$ m. If the temperature of the body is raised to 1400 K, the wavelength of maximum emitted energy will be

1. 1.02 μm

2. 16.32 μm

3. 8.16 μm

4. 2.04 μm

Q.

Wavelength of light used in an optical instrument are ${\lambda }_1=4000\dot{A}$ and ${\lambda }_2=5000\dot{A}$ then ratio of their respective resolving power is

1. 5 : 4

2. 16:25

3. 25: 16

4. 4 : 5

Q.

Which one of the following is the use of a concave lens?

1. Magnifying glass

2. Optical instruments.

3. In theatre spotlights

4. all of the above

Q.

Figure shows the behaviour of light rays with respect to a thin plano-convex lens whose plane surface is silvered as shown in the figure. If the refractive index of the material of the lens is 1.5. choose the correct option(s).

1. The focal length of the silvered lens (which acts as a mirror) is 10 cm.

2. Radius of curvature of the curved part of the lens is 10 cm.

3. In the silvered lens, rays fall normally on the silvered surface.

4. The focal length of the lens (without silvering) is 20 cm.

Q. A simple telescope, consisting of an objective of focal length $60cm$ and a single eye lens of focal length $5cm$ is focussed on a distant object in such a way that parallel rays emerge from the eye lens. If the object makes an angle of $2^{\circ }$ at the objective, the angular width of the image is

1. ${10}^{\circ }$
2. ${24}^{\circ }$
3. ${50}^{\circ }$
4. None of the above

Q. A single converging lens is held close to the eye for use as a mangnifying glass. For maximum magnifying power, the lens must be positioned, so that

1. object is just beyond the principal focus of the lens.
2. the image is at the near point of the eye.
3. the image is at infinity.
4. the image is at the principal focus of the lens.

Q. A telescope of diameter 2m uses light of wavelength $5000\dot{A}$ for viewing stars. The minimum angular separation between two stars whose image is just resolved by this telescope is

1. $0.25\times {10}^{-6}rad$
   
2. $0.31\times {10}^{-6}rad$
   
3. $5.0\times {10}^{-3}rad$
4. $4\times {10}^{4}rad$
   

Q. aperture of human eye is 0.2 cm. the minimum magnifying power of a visual telescope whose objective has diameter 100 cm is

Q. An eye specialist prescribes spectacles having a combination of convex lens of focal length $40\text{cm}$ in contact with a concave lens of focal length $25\text{cm}$. The power of this lens combination in diopter is

1. $+1.5$
2. $-1.5$
3. $+6.67$
4. $-6.67$

Q. To produce characteristic X-rays using a tungsten target in an X-ray generator, the energy of the characteristic radiation is $\text{eV}.$
(The binding energy of the innermost electron in tungsten is $40\text{keV}.)$

Q.

The aperture of the human eye is $2mm$. Assuming the mean wavelength of light to be $5000A^{°}$ , the angular limit of resolution of the eye is nearly

1. $1$ minute

2. $2$ minute

3. $0.5$ minute

4. $1.5$ minute

Q. 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 electrons(3) Its resolving power is inversely proportional to wavelength of electrons(4) Magnification attained with the help of it is of the order of 10^{

Q. Two coaxial diverging lenses are kept as shown in figure. An object $O$ is placed , then the final image formed will be

1. Virtual for any value of $d_1$ and $d_2$
2. Real for any value of $d_1$ and $d_2$
3. Virtual or real depends on $d_1$ and $d_2$ only
4. Virtual or real depends on $d_1$ and $d_2$ and also on the focal lengths of the lens

Q. Given below are two statements : One is labelled as Assertion $A$ and the other is labelled as reason $R$.

$A$ : For a simple microscope, the angular size of the object equals the angular size of the image.

$R$ : Magnification is achieved as the small object can be kept much closer to the eye than $25\text{cm}$ and hence it subtends a large angle.

In the light of the above statements, choose the most appropriate answer from the options given below.

1. Both $A$ and $R$ are true, but $R$ is NOT the correct explanation of $A$.
2. Both $A$ and $R$ are true, and $R$ is the correct explanation of $A$.
3. $A$ is true, but $R$ is false.
4. $A$ is false, but $R$ is true.

Q.

Find the minimum colatitude which can directl receive a signal from a goestationary satellite.