Tag: sign convention for the measurement of distances

Questions Related to sign convention for the measurement of distances

A concave lens of focal length $f$ produces an image $(1/x)$ of the size of the object. The distance of the object from the lens is

physics reflection of light in spherical mirrors sign convention for mirrors sign convention for spherical mirrors sign convention for the measurement of distances

  1. $(x - 1)f$

  2. $(x + 1)f$

  3. $\dfrac{(x - 1)}{x}$ $f$

  4. $\dfrac{(x + 1)}{x}$ $f$

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Correct Option: B

A concave spherical mirror, forms a 40 cm high real image of an object, whose height is 10 cm. The radius of the mirror is 60 cm. Find the distance from the object to its image.

physics reflection of light in spherical mirrors sign convention for mirrors sign convention for spherical mirrors sign convention for the measurement of distances

  1. 97.5 cm

  2. 75 cm

  3. 90cm

  4. 177.5 cm

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Correct Option: D

When a ray of light parallel to the principle axis is incident on a concave mirror$,$ the reflected ray

physics reflection of light in spherical mirrors sign convention for mirrors sign convention for spherical mirrors sign convention for the measurement of distances

  1. Passes through C

  2. Passes through F

  3. Passes midway between P and F

  4. retraces its path

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Correct Option: B

A mirror faces the negative x-axis. (Normal to its reflecting surface is$- \hat { i } )$  While a particle starts moving such that its image is formed in the mirror. At a certain instant the velocity of the particles is $3 \hat { i } + 4 \hat { j } + 5 \hat { k }$ and that of the mirror is $\hat { 1 } - \hat { j } + \hat { k }$ Choose the correct options.

physics reflection of light in spherical mirrors sign convention for mirrors sign convention for spherical mirrors sign convention for the measurement of distances

  1. Magnitude of relative velocity of the image w.r.t mirrror is$\sqrt { 45 }$

  2. Magnitude of relative velocity of image w.r.t object is 4

  3. Magnitude of relative velocity of image w.r.t mirrror is $\sqrt { 45 }$

  4. Absolute velocity of the image w.r.t ground is$\sqrt { 42 }$

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Correct Option: A,C
Explanation:

$\begin{array}{l} In\, y-direction \ { V _{ o } }={ V _{ i } } \ \Rightarrow { V _{ i } }=4\widehat { j }  \ In\, z-direction \ { V _{ i } }={ V _{ o } } \ \Rightarrow { V _{ i } }=5\widehat { k }  \ In\, x-direction \ { V _{ IM } }=-{ V _{ oM } } \ \Rightarrow { V _{ IM } }=-{ V _{ oM } } \ \Rightarrow { V _{ I } }-{ V _{ M } }={ V _{ M } }-{ V _{ o } } \ \Rightarrow { V _{ I } }=2{ V _{ M } }-{ V _{ o } } \ =2\left[ { \widehat { i }  } \right] -3\left[ { \widehat { i }  } \right]  \ =-\widehat { i }  \ \therefore \overrightarrow { { V _{ I } } } =-\widehat { i } +4\widehat { j } +5\widehat { k }  \ \therefore \overrightarrow { { V _{ iM } } } =-2\widehat { i } +5\widehat { j } +4\widehat { k }  \ \therefore \left| { \overrightarrow { { V _{ iM } } }  } \right| =\sqrt { 45 }  \end{array}$

Hence,
option $(A)$ and $(C)$ are both correct answer.

A thin. rod of length f/ 3 is placed along the principal axis of a concave mirror of focal length f such that its image which is real and elongated, just touches one end of the rod. What is its magnification ?

physics reflection of light in spherical mirrors sign convention for mirrors sign convention for spherical mirrors sign convention for the measurement of distances

  1. +2

  2. -3

  3. -1.5

  4. -2

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Correct Option: C

An astronomical telescope has an objective of focal length $200 \,cm$ and an eye piece of focal length $4\,cm$ The telescope is focused to see an object $10\, km$ from the objective,.The final image is formed at infinity. The length of the tube and angular magnification produced by it is

physics reflection of light in spherical mirrors sign convention for mirrors sign convention for spherical mirrors sign convention for the measurement of distances

  1. $204\, cm, -50$

  2. $200\, cm, -50$

  3. $204\, cm, -100$

  4. $200\, cm, -100$

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Correct Option: A

Let the equation connecting object distance $u$, image distance $v$ and focal length $f$ for a lens be $\dfrac{1}{u} + \dfrac{1}{v} = \dfrac{1}{f}$. A student measures values of $u$ and $v$, with their associated uncertainties.
These are $u = 50\ mm \pm 3\ mm, v = 200\ mm \pm 5\ mm$. He calculates the value of $f$ as $40\ mm$. What is the uncertainty in this value?

physics reflection of light in spherical mirrors sign convention for mirrors sign convention for spherical mirrors sign convention for the measurement of distances

  1. $\pm 2.1\ mm$

  2. $\pm 3.4\ mm$

  3. $\pm 4.5\ mm$

  4. $\pm 6.8\ mm$

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Correct Option: A

A man has a concave shaving mirror of focal length $0.2$ m. How far should the mirror be held from his face in order to give an image of two fold magnification? 

physics reflection of light in spherical mirrors sign convention for mirrors sign convention for spherical mirrors sign convention for the measurement of distances

  1. $0.1$ m

  2. $0.2$ m

  3. $0.3$ m

  4. $0.4$ m

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Correct Option: A
Explanation:

Concave shaving mirror  $f = 0.2m$

Magnification,$m = 2$
$m = \dfrac{-v}{u}$

$2 = \dfrac{-v}{u}$
$v = -2u$
Using mirror formula 
$\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$

$- \dfrac{1}{0.2} = -\dfrac{1}{2u} + \dfrac{1}{u}$

$-\dfrac{1}{0.2}=\dfrac{1}{2u}$

$u = -0.1m$
i.e shaving mirror should be 10cm ahead of man

A small candle 2.5 cm in size is placed 27 cm in front of a concave mirror of radius of curvature 36 cm.

physics reflection of light in spherical mirrors sign convention for mirrors sign convention for spherical mirrors sign convention for the measurement of distances

  1. The distance from the mirror, should a screen be placed in order to receive a sharp image is-54 cm.

  2. The nature of image is  virtual inverted w.r.t. object.

  3. The image formed is 8 times highest the object.

  4. The image formed is 3 times highest the object.

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Correct Option: A

An object is placed at a distance of 36 cm from a convex mirror . A plane mirror is placed in between , so that the two virtual image so formed coincide . If the plane mirror is at a distance of 24 cm from the object , find the radius of curvature of the convex mirror . 

physics reflection of light in spherical mirrors sign convention for mirrors sign convention for spherical mirrors sign convention for the measurement of distances

  1. $43 cm$

  2. $36 cm$

  3. $78 cm$

  4. $97 cm$

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Correct Option: B