Tag: principle of reversibility of path of light

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Questions Related to principle of reversibility of path of light

Multiple choice physics light : reflection and refraction from plane surface introduction to light and mirror magic with mirrors image formation by plane mirror principle of reversibility of path of light refractive index

A plane mirror is in a vertical plane and is rotating about a vertical axis at 100 mm horizontal beam of light is incident on the mirror. The reflected beam will rotate at

  1. $100 rpm$

  2. $141 rpm$

  3. $0 rpm$

  4. $200 rpm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When a mirror rotates at an angular velocity omega, the reflected ray rotates at an angular velocity of 2*omega. Therefore, if the mirror rotates at 100 rpm, the reflected beam rotates at 200 rpm.

Multiple choice physics light : reflection and refraction from plane surface introduction to light and mirror magic with mirrors image formation by plane mirror principle of reversibility of path of light refractive index

When a mirror is rotated through an angle, the reflected ray moves through double that angle, the instrument based on the above principle is :

  1. Periscope

  2. Odometer

  3. Refractometer

  4. Sextant
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A periscope is based on the principle of reflection.

An Odometer is used to measure the distance travelled by a vehicle.
A Refractometer is based on the principle of refraction (Snell'slaw).
A Sextant is used to measure the angle between two visible objects. Baesd on the principle that when a mirror is rotated through an angle the reflected ray moves through double of that angle.

Multiple choice physics light : reflection and refraction from plane surface introduction to light and mirror magic with mirrors image formation by plane mirror principle of reversibility of path of light refractive index

A source of light lies on the angle bisector of two plane mirrors inclined at an angle $\theta$. The values of $\theta$, so that the light reflected from one mirror does not reach the other mirror will be

  1. $\theta \geq 120^0$

  2. $\theta \geq 90^0$

  3. $\theta \leq 120^0$

  4. $\theta < 30^0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For the light reflected from one mirror not to reach the other, the angle of incidence on the second mirror must be such that it cannot be reflected. This occurs when the angle between the mirrors is 120 degrees or more.

Multiple choice physics light : reflection and refraction from plane surface introduction to light and mirror magic with mirrors image formation by plane mirror principle of reversibility of path of light refractive index

In a Michelson experiment for measuring speed of light, the distance traveled by light between two reflections from the rotating mirror is 4.8 km. The rotating mirror has a shape of a regular octagon. At what minimum angular speed of the mirror (other than zero) the image is formed at the position where a non-rotating mirror forms it?

  1. $780$ $rev/s$

  2. $7800$ $rev/s$

  3. $690$ $rev/s$

  4. $7500$ $rev/s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Minimum angular speed $ f=\dfrac { c }{ dN }$


$ =\dfrac { 3\times { 10 }^{ 8 } }{ 4.8\times { 10 }^{ 3 }\times 8 }$

$ =7812rev/s\cong 7800rev/s$

Multiple choice physics light : reflection and refraction from plane surface introduction to light and mirror magic with mirrors image formation by plane mirror principle of reversibility of path of light refractive index

A plane mirror which rotates $10^4$ times per minute reflects light on to a stationary mirror $50$ m away. This mirror reflects the light normally so that it strikes the rotating mirror again. The image observed in the rotating mirror is shifted through $2.4$ minutes from the position it occupies. When the rotating mirror is stationary, what is the speed of light?

  1. $3\times 10^8$ m/s

  2. $4\times 10^8$ m/s

  3. $5\times 10^8$ m/s

  4. $6\times 10^8$ m/s
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a classic Fizeau or Michelson-type experiment setup. Using the formula for the speed of light c = 4*N*D*theta, where N is frequency, D is distance, and theta is the deflection angle, the calculation yields 3*10^8 m/s.

Multiple choice physics light : reflection and refraction from plane surface introduction to light and mirror magic with mirrors image formation by plane mirror principle of reversibility of path of light refractive index

A flat mirror revolves at a constant angular velocity making $n=0.4$ revolutions per second. With what velocity (in $ms^{-1}$ ) will a light spot move along a spherical screen with a radius of $15$ metres, if the mirror is at the centre of curvature of the screen?

  1. $37.7$

  2. $60.3$

  3. $68.7$

  4. $75.4$

  5. $90.4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$\because$ Angular velocity of mirror = $0.4rev/s$
$\Rightarrow 0.4\times 2\pi=0.8\pi\,rad/s$
$\because$ Angular velocity of reflected ray
$\Rightarrow 2\times 0.8\pi=1.6\pi\,rad/s$
Hence, velocity of light spot over the screen
$v=rw=15\times 1.6\pi=75.4m/s$
Multiple choice physics light : reflection and refraction from plane surface introduction to light and mirror magic with mirrors image formation by plane mirror principle of reversibility of path of light refractive index

Light incident on a rotating mirror M is returned to a fixed mirror N placed 22.5 km away from M. The fixed mirror reflects it back to M (along the same path) which in turn reflects the light again along a direction that makes an angle of $\displaystyle { 27 }^{ o }$ with the incident direction. The speed of rotation of the mirror is: 

  1. 250 revolutions $\displaystyle { s }^{ -1 }$

  2. 500 revolutions $\displaystyle { s }^{ -1 }$

  3. 1000 revolutions $\displaystyle { s }^{ -1 }$

  4. 125 revolutions $\displaystyle { s }^{ -1 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Suppose the number of revolutions are n. The angle between 2 positions of the rotating mirror  = $\dfrac { 1 }{ 2 } \times 27\quad degrees$.

Since the angle of rotation of mirror is half the angle through which the reflected ray rotates.

The time taken by the mirror in rotating through an angle $\theta $ is given by $t=\dfrac { \theta  }{ 2\pi n } =\dfrac { 13.5\quad degrees }{ 2\times 180\times n } sec.$ -- Eqn 1

This is also the time taken by the light to travel from original point to the fixed mirror and back, thus

$t=\dfrac { 2d }{ c } =\dfrac { 2\times 22500 }{ 3\times { 10 }^{ 8 } } [d=22.5\quad km=22500m\quad and\quad c=3\times { 10 }^{ 8 }m/s]$ -- Eqn 2

From eqns 1 and 2,

$\dfrac { 13.5 }{ 2\times 180\times n } =\dfrac { 2\times 22500 }{ 3\times { 10 }^{ 8 } } $

or n = $\dfrac { 13.5\times 3\times { 10 }^{ 8 } }{ 2\times 180\times 2\times 22500 } =\dfrac { 40.5\times { 10 }^{ 8 } }{ 16200000 } =\dfrac { 40500\times { 10 }^{ 5 } }{ 162\times { 10 }^{ 5 } } =250\quad revolutions/s$.

Hence, the number of revolutions are 250 revolutions/s.
Multiple choice physics light : reflection and refraction from plane surface introduction to light and mirror magic with mirrors image formation by plane mirror principle of reversibility of path of light refractive index

The reflective surface is given by y $=$ 2 sinx. The reflective surface is facing positive x-axis. What is the least values of co ordinate of the point where a ray parallel to positive x axis becomes parallel to positive y axis after reflection 2. 

  1. $\left ( \dfrac{\pi }{3},\sqrt{3} \right )$

  2. $\left ( \dfrac{\pi }{2},\sqrt{2} \right )$

  3. $\left ( \dfrac{\pi }{3},\sqrt{2} \right )$

  4. $\left ( \dfrac{\pi }{4},\sqrt{2} \right )$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$m (L _1) = 2 cos x _o$


$m(N) = \dfrac {+1}{2 cos x _o}$

$m(N) = \dfrac {+1}{2 cos x _o} = 1$

$cos x _o = \dfrac {1}{2}$

      $x _o = \dfrac {\pi}{3}$

        $y = 2sin (\dfrac {\pi}{3}) = \sqrt {3}$

Multiple choice physics light : reflection and refraction from plane surface introduction to light and mirror magic with mirrors image formation by plane mirror principle of reversibility of path of light refractive index

The angle between the incident and reflected rays is $90^o$. If the plane mirror is rotated by $10^o$ about O in the anti-clockwise direction in the plane perpendicular to the mirror, then the angle between the incident and reflected rays will be _______$^0$.

  1. 70

  2. 100

  3. 90

  4. 110

  5. 80
Reveal answer Fill a bubble to check yourself
A,D Correct answer
Explanation

If the plane mirror is rotated by 10 degrees about O in the anti-clockwise direction then the angle between the incident and reflected rays will be reduced by 20 degrees. So the angle between incident and reflected ray will be 70 degrees.
If the plane mirror is rotated by 10 degrees in clockwise direction, then the angle between the incident and reflected rays increases by 20 degrees and becomes 110 degrees.

Multiple choice physics light : reflection and refraction from plane surface introduction to light and mirror magic with mirrors image formation by plane mirror principle of reversibility of path of light refractive index

When a plane mirror is rotated through an angle $\theta$, the reflected ray rotates through an angle $2\theta$. Then the size of the image 

  1. is halved

  2. is doubled

  3. remains unchanged

  4. is quadrupled
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When a plane mirror is rotated through an angle $\theta$ , then the reflected ray rotates through an angle 2$\theta$; but the size of the image remain the same.