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Q. No.A car is moving with at a constant speed of \(60~\text{km/h}\) on a straight road. Looking at the rear view mirror, the driver finds that the car following him is at a distance of \(100~\text{m}\) and is approaching with a speed of \(5~\text{km/h}\). In order to keep track of the car in the rear, the driver begins to glance alternatively at the rear and side mirror of his car after every \(2~\text{s}\) till the other car overtakes. If the two cars were maintaining their speeds, which of the following statement (s) is/are correct?
1.
The speed of the car in the rear is \(65~\text{km/h}\).
2.
In the side mirror the car in the rear would appear to approach with a speed of \(5~\text{km/h}\) to the driver of the leading car.
3.
In the rear view mirror the speed of the approaching car would appear to decrease as the distance between the cars decreases.
4.
In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases.
Subtopic: Reflection at Spherical Surface |
Level 3: 35%-60%
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There are certain material developed in laboratories which have a negative refractive index (see figure). A ray incident from air (medium 1) into such a medium (medium 2) shall follow a path given by,
| 1. |  |
| 2. |  |
| 3. |  |
| 4. |  |
Subtopic: Refraction at Plane Surface |
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Consider an extended object immersed in water contained in a plane trough. When seen from close to the edge of the trough the object looks distorted because
Choose the correct option:
1. (a), (d)
2. (a), (b), (c)
3. (b), (d)
4. (c), (d)
| (a) | the apparent depth of the points close to the edge are nearer the surface of the water compared to the points away from the edge. |
| (b) | the angle subtended by the image of the object at the eye is smaller than the actual angle subtended by the object in air. |
| (c) | some of the points of the object far away from the edge may not be visible because of total internal reflection. |
| (d) | water in a trough acts as a lens and magnifies the object |
Choose the correct option:
1. (a), (d)
2. (a), (b), (c)
3. (b), (d)
4. (c), (d)
Subtopic: Total Internal Reflection |
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A rectangular block of glass \(ABCD\) has a refractive index \(1.6\). A pin is placed midway on the face \(AB\) (see figure). When observed from the face \(AD\), the pin shall
Choose the correct option:
| (a) | appear to be near \(A\). |
| (b) | appear to be near \(D\). |
| (c) | appear to be at the centre of \(AD\). |
| (d) | not be seen at all. |
| 1. | (a), (c) | 2. | (b), (d) |
| 3. | (c), (d) | 4. | (a), (d) |
Subtopic: Total Internal Reflection |
Level 3: 35%-60%
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Between the primary and secondary rainbows, there is a dark band known as Alexandar’s dark band. This is because
a. light scattered into this region interfere destructively.
b. there is no light scattered into this region.
c. light is absorbed in this region.
d. angle made at the eye by the scattered rays with respect to the incident light of the sun lies between approximately 42° and 50°.
Choose the correct option:
1. (a), (d)
2. (a), (c), (d)
3. (b), (d)
4. (c), (d)
a. light scattered into this region interfere destructively.
b. there is no light scattered into this region.
c. light is absorbed in this region.
d. angle made at the eye by the scattered rays with respect to the incident light of the sun lies between approximately 42° and 50°.
Choose the correct option:
1. (a), (d)
2. (a), (c), (d)
3. (b), (d)
4. (c), (d)
Subtopic: Total Internal Reflection |
Level 3: 35%-60%
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A magnifying glass is used, as the object to be viewed can be brought closer to the eye than the normal near point. This results in
a. a larger angle to be subtended by the object at the eye and hence viewed in greater detail.
b. the formation of a virtual erect image.
c. increase in the field of view.
d. infinite magnification at the near point.
Choose the correct option:
1. (a), (b)
2. (a), (c), (d)
3. (b), (d)
4. (c), (d)
a. a larger angle to be subtended by the object at the eye and hence viewed in greater detail.
b. the formation of a virtual erect image.
c. increase in the field of view.
d. infinite magnification at the near point.
Choose the correct option:
1. (a), (b)
2. (a), (c), (d)
3. (b), (d)
4. (c), (d)
Subtopic: Lenses |
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An astronomical refractive telescope has an objective of focal length \(20~\text{m}\) and an eyepiece of focal length \(2~\text{cm}\).
Choose the correct option from the given ones:
| (A) | The length of the telescope tube is \(20.02~\text{m}\). |
| (B) | The magnification is \(1000\). |
| (C) | The image formed is inverted. |
| (D) | An objective of a larger aperture will increase the brightness and reduce chromatic aberration of the image. |
| 1. | (A) and (D) only |
| 2. | (A), (B) and (C) only |
| 3. | (B) and (D) only |
| 4. | (C) and (D) only |
Subtopic: Telescope |
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Consider a ray of light incident from air onto a slab of glass (refractive index \(n\)) of width \(d\), at an angle \(\theta\). The phase difference between the ray reflected by the top surface of the glass and the bottom surface is
1. \(\dfrac{4 \pi d}{\lambda}\left(1-\dfrac{1}{n^2} \sin ^2 \theta\right)^{1 / 2}+\pi \)
2. \(\dfrac{4 \pi d}{\lambda}\left(1-\dfrac{1}{n^2} \sin ^2 \theta\right)^{1 / 2} \)
3. \(\dfrac{4 \pi d}{\lambda}\left(1-\dfrac{1}{n^2} \sin ^2 \theta\right)^{1 / 2}+\dfrac{\pi}{2} \)
4. \(\dfrac{4 \pi d}{\lambda}\left(1-\dfrac{1}{n^2} \sin ^2 \theta\right)^{1 / 2}+2 \pi\)
1. \(\dfrac{4 \pi d}{\lambda}\left(1-\dfrac{1}{n^2} \sin ^2 \theta\right)^{1 / 2}+\pi \)
2. \(\dfrac{4 \pi d}{\lambda}\left(1-\dfrac{1}{n^2} \sin ^2 \theta\right)^{1 / 2} \)
3. \(\dfrac{4 \pi d}{\lambda}\left(1-\dfrac{1}{n^2} \sin ^2 \theta\right)^{1 / 2}+\dfrac{\pi}{2} \)
4. \(\dfrac{4 \pi d}{\lambda}\left(1-\dfrac{1}{n^2} \sin ^2 \theta\right)^{1 / 2}+2 \pi\)
Subtopic: Refraction at Plane Surface |
Level 3: 35%-60%
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The optical density of turpentine is higher than that of water while its mass density is lower. Figure shows a layer of turpentine floating over water in a container. For which one of the four rays incident on turpentine in Figure, the path shown is correct?
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
Subtopic: Refraction at Plane Surface |
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The direction of ray of light incident on a concave mirror is shown by \(\mathrm{PQ}\) while directions in which the ray would travel after reflection is shown by four rays marked \(1,2,3\) and \(4\). Which of the four rays correctly shows the direction of reflected ray?
| 1. | \(1\) | 2. | \(2\) |
| 3. | \(3\) | 4. | \(4\) |
Subtopic: Reflection at Spherical Surface |
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