Light Test

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Light Test - 31

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Weekly Quiz Competition

Question 1
1 / -0

Image seen by a periscope is:

A
laterally inverted

B
longitudinally inverted

C
both A and B

D
neither A nor B

Solution

The image seeing by a periscope is a reflected image and not laterally inverted.
In the periscope, light hits the top mirror at 45 degrees and reflects away at the same angle. The light then bounces down to the bottom mirror. When that reflected light hits the second mirror it is reflected again at 45 degrees, right into our eye. Hence, the image is due to the reflections at two mirrors. So, lateral inversion happens twice consecutively and the final image is neither laterally inverted nor longitudinally inverted.
Question 2
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The incident ray and the reflected ray from a mirror is mutually perpendicular to each other. Find the angle of incidence.

A
$$0^{\circ}$$

B
$$90^{\circ}$$

C
$$30^{\circ}$$

D
$$45^{\circ}$$

Solution

The angle of incidence is the angle between this normal line and the incident ray; the angle of reflection is the angle between this normal line and the reflected ray. According to the law of reflection, the angle of incidence equals the angle of reflection.
So, $$i=r$$
Given, $$i+r=90^0$$
$$\implies$$ $$i+i=90^0$$
or, $$2i=90^0$$
or, $$i=45^0$$
Question 3
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How many images are formed for a point object kept in between two plane mirrors $$M_1$$ and $$M_2$$, at right angles to each other ?

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

If two plane mirrors are placed together on one of their edges so as to form a right angle mirror system, 3 images are formed.
$$n=\dfrac{360}{90} - 1=3$$
Right angle mirrors will allow a maximum of two reflections of light from the object. But as the angle decreases, three, four, and even more reflections can occur. Below is the diagrammatic representation.
Question 4
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A light ray is incident normally on a plane mirror.
(a) What is the angle of incidence?
(b) What is the path of reflected ray?

A
$$(a) 180^{\circ}, (b)$$ same as incident ray

B
$$(a)180^{\circ}, (b)$$ opposite to incident ray

C
$$(a) 0^{\circ}, (b)$$ opposite to incident ray

D
$$(a) 0^{\circ}, (b)$$ same as incident ray

Solution

Case (a):
If a ray of light is incident normal to the surface of the plane mirror, then the angle of incidence is $$0^0$$, as the normal passes perpendicularly to the mirror.
Case (b):
The Second Law of Reflection states that the angle of incidence is always equal to the angle of reflection. Therefore, the angle of reflection is same as the angle of incidence, that is, $$0^0$$. So, the reflected ray will retrace the path of the incident ray.
Question 5
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How many plane mirrors are used in a periscope ? How are they arranged relative to each other ?

A
Two, perpendicular to each other.

B
Four, parallel to each other.

C
Four, perpendicular to each other.

D
Two, parallel to each other.

Solution

A periscope is an instrument for observation over, around or through an object, obstacle or condition that prevents direct line-of-sight observation from an observer's current position.
A simple periscope is just a long tube with a mirror at each end. The mirrors are fitted into each end of the tube as shown in the figure.
Hence, there are 2 plane mirrors used which are placed parallel to each other.
Question 6
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State the number of images of an object placed between two mirrors, formed in each case when mirrors are inclined to each other at $$(a) 90^{\circ}$$ and $$(b) 60^{\circ}$$.

A
$$(a) 4$$, $$(b) 6$$

B
$$(a) 3$$, $$(b) 5$$

C
$$(a) 2$$, $$(b) 3$$

D
$$(a) 1$$, $$(b) 2$$

Solution

(a) When $$\theta=90^0$$,
$$n=\dfrac{360}{90} - 1=3$$

(b) When $$\theta=60^0$$
$$n=\dfrac{360}{60} - 1=5$$
Question 7
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Two plane mirrors are placed making an angle $$\theta $$ in between them. What is the expression for the number of images formed of an object placed in between the mirrors?

A
$$n$$ if $$\displaystyle n= \frac {360^{\circ}}{\theta ^{\circ}}$$ is odd and object is asymmetrically placed

B
$$n-1$$ if $$n = \frac {360^{\circ}}{\theta ^{\circ}}$$ is even, or odd and object is symmetrically placed.

C
Both A & B

D
None

Solution

If the image of an object is viewed in two plane mirrors that are inclined to each other, more than one image is formed. The number of images depends on the angle between the two mirrors.
The number of images formed in two plane mirrors inclined at an angle A to each other is given by the below formula.
Number of images $$n=\dfrac{360}{A} - 1$$
The number of images formed $$n=\dfrac{360}{A} - 1$$, if $$\dfrac{360}{A}$$ is an even integer.
If $$\dfrac{360}{A}$$ is odd integer, the number of images formed $$n=\dfrac{360}{A} - 1$$ when the object is kept symmetrically, and $$n=\dfrac{360}{A}$$ when object is kept asymmetrically.
If $$\dfrac{360}{A}$$ is a fraction, the number of images formed is equal to its integral part.
As the angle gets smaller (down to 0 degrees when the mirrors are facing each other and parallel) the smaller the angle the greater the number of images.
Question 8
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The final image formed in a periscope is:

A
both real and virtual

B
reflected

C
real

D
none of these

Solution

A simple periscope is just a long tube with a mirror at each end. The mirrors are fitted into each end of the tube at an angle of exactly 45 degrees so that they face each other.
In the periscope, light hits the top mirror at 45 degrees and reflects away at the same angle. The light then bounces down to the bottom mirror. When that reflected light hits the second mirror it is reflected again at 45 degrees, right into our eye.
Light is always reflected away from a mirror at the same angle that it hits the mirror.
Hence, the image formed in a periscope is reflected, and not real.
Question 9
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An object is placed
$$(i)$$ Asymmetrically
$$(ii)$$ Symmetrically, between two plane mirrors inclined at an angle of $$50^{\circ}$$. Find the number of images formed.

A
$$(1) 7$$, $$(ii) 7$$

B
$$(1) 6$$, $$(ii) 6$$

C
$$(1) 6$$, $$(ii) 7$$

D
$$(1) 7$$, $$(ii) 6$$

Solution

Case (a):
Two plane mirrors places asymmetrically at 50 degrees.
Number of images $$=\dfrac{360}{50}=7$$ (highest integral value)
Case (b):
Two plane mirrors places symmetrically at 50 degrees.
Number of images $$=\dfrac{360}{50} - 1=6$$ (highest integral value)
Question 10
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Rectilinear propagation of light is :

A
Property of travelling in curved lines

B
Property of travelling in straight lines

C
Ability to bend around obstacles

D
Displaying the phenomenon of diffraction

Solution

Rectilinear propagation of light is the tendency of light to travel in a straight line.