Reflection Test

Result

Reflection Test - 5

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Question 1/10
1 / -0

A light ray I is incident on a plane mirror M. The mirror is rotated in the direction as shown in the figure by an arrow at a frequency 9 / π rev / sec. The light reflected by the mirror is received on the wall W at a distance 10 m from the axis of rotation. When the angle of incidence becomes 37^o, find the speed of the spot (a point) on the wall?

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A
10 m/s

Correct

Wrong

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B
1000 m/s

Correct

Wrong

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C
500 m/s

Correct

Wrong

Skipped
D
None of these

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Solutions

For a given incident ray, if the mirror is rotated through an angle θ , then the reflected ray turns through an angle of 2 θ . So if angular speed of mirror is ω then the angular speed by which the reflected ray is rotated is 2 ω.

when
Question 2/10
1 / -0

An object is moving towards a concave mirror of focal length 24 cm. When it is at a distance of 60 cm from the mirror its speed is 9cm/s, the speed of its image at that instant is :

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A
4 cm/s towards the mirror

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Wrong

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B
9 cm/s towards the mirror

Correct

Wrong

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C
4 cm/s away from the mirror

Correct

Wrong

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D
9 cm/s away from the mirror

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Solutions

For a concave mirror, we use the mirror formula

Now, given u=−60 cm , f = −24 cm

Putting the values in the expression,

This gives, v = −40 cm

Now, for relating the velocities, we differentiate the mirror formula,to obtain,

Now, u′=9cm/s

Substituting these values, we get
Question 3/10
1 / -0

In the figure shown a thin parallel beam of light is incident on a plane mirror m₁ at small angle 'θ'. m₂ is a concave mirror of focal length 'f '. After three successive reflections of this beam the x and y coordinates of the image is :

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A
x = f – d, y = fθ

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B
x = d + f, y = fθ

Correct

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C
x = f – d, y = – f θ

Correct

Wrong

Skipped
D
x = d – f, y = – f θ

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Solutions

After I^st reflection (from plane mirror)

Parallel beam of light strick on a concave mirror.

After II^nd reflection (from concave mirror)

Image is formed at focus and shifted by a distance f θ (⟂ to principal axis)

For III^rdreflection

Object is placed at a distance | f.d| from a plane mirror.
Question 4/10
1 / -0

The focal length of a concave mirror is f and the distance from the object to the principal focus is x. The ratio of the size of the image to the size of the object is :

Correct

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A

Correct

Wrong

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B

Correct

Wrong

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C

Correct

Wrong

Skipped
D

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Solutions

As we know,
Question 5/10
1 / -0

A rear mirror of a vehicle is cylindrical having radius of curvature 10 cm. The length of arc of curved surface is also 10 cm. If the eye of the driver is assumed to be at a large distance from the mirror, then the field of view in radians is

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A
0.5

Correct

Wrong

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B
1

Correct

Wrong

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C
2

Correct

Wrong

Skipped
D
4

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Solutions
Question 6/10
1 / -0

An object 0.5 cm high is placed 30 cm from a convex mirror whose focal length is 20 cm. Find the position, size and nature of the image.

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A
12 cm, 0.2 cm

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B
18 cm, 0.2 cm

Correct

Wrong

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C
6 cm, 0.5 cm

Correct

Wrong

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D
5 cm, 0.1 cm

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Solutions

We have,
Distance of object from the mirror, u = –30 cm;
Distance of image, v = ?
Focal length, f = + 20 cm
We know, using the mirror formula,

The image is virtual and erect as, it is formed at a distance of 12 cm behind the mirror.

Now, size if the object, O = 0.5 cm
sixe of the image = I

Hence, the height of the image = + 0.2 cm.

The positive sign indicates that the image is erect is smaller in size
Question 7/10
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In the figure shown, the image of a real object is formed at point I. AB is the principal axis of the mirror. The mirror must be:

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A
concave and placed towards right of I

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B
concave and placed towards left of O

Correct

Wrong

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C
convex and placed towards right of I

Correct

Wrong

Skipped
D
convex and placed towards left of I

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Solutions

In the question, the image is inverted and magnified, so, it is formed due to concave mirror with image and object on the same side of mirror and the object closer to the mirror.
Question 8/10
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Two plane mirrors A and B are aligned parallel to each other, as shown in fig. A light ray is incident at an angle of 30^o at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflection (including the first one) before it emerges out is:

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A
28

Correct

Wrong

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B
30

Correct

Wrong

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C
32

Correct

Wrong

Skipped
D
34

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Solutions

Let the distance covered by the ray after reflection from a surface be d.

From the first law of reflection and alternate angle property, all the angles shown in the figure are equal to 30⁰.

From the figure,
Question 9/10
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An object O is placed in front of a plane mirror. A person looks into the mirror as shown. At what position is the image of O is observed by person?

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A
A

Correct

Wrong

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B
B

Correct

Wrong

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C
C

Correct

Wrong

Skipped
D
D

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Solutions

For image to be observed by person, the reflected or refracted rays must reach the person's eye, which confirms that image of O as observed by person is at B.
Question 10/10
1 / -0

An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is 30 cm, it is found that that is no parallax between the images formed by the two mirrors. What is the radius of curvature of the convex mirror?

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A
25cm

Correct

Wrong

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B
7cm

Correct

Wrong

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C
18cm

Correct

Wrong

Skipped
D
27cm

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Solutions

As shown in figure, the plane mirror will form erect and virtual image of same size at a distance of 30 cm behind it. So, the distance of image formed by plane mirror from convex mirror will be

PI = MI − MP

But as, MI = MO

PI = MO − MP = 30 − 20 = 10 cm

Now, as this image coincides with the image formed by convex mirror, therefore for convex mirror,

u = −50 cm; v = + 10 cm

Question 1/10

10 m/s

1000 m/s

500 m/s

None of these

Question 2/10

4 cm/s towards the mirror

9 cm/s towards the mirror

4 cm/s away from the mirror

9 cm/s away from the mirror

Question 3/10

x = f – d, y = fθ

x = d + f, y = fθ

x = f – d, y = – f θ

x = d – f, y = – f θ

Question 4/10

Question 5/10

0.5

1

2

4

Question 6/10

12 cm, 0.2 cm

18 cm, 0.2 cm

6 cm, 0.5 cm

5 cm, 0.1 cm

Question 7/10

concave and placed towards right of I

concave and placed towards left of O

convex and placed towards right of I

convex and placed towards left of I

Question 8/10

28

30

32

34

Question 9/10

A

B

C

D

Question 10/10

25cm

7cm

18cm

27cm