Tag: problems on mirror and magnification formula

Questions Related to problems on mirror and magnification formula

A flim projector magnifies a flim of area $100 $ square centimeter on screen. If linear magnification is $4$ then area of magnified image on screen will be-

physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. $1600 sq. cm$

  2. $800 sq. cm$

  3. $400 sq. cm$

  4. $200 sq. cm$

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Correct Option: A
Explanation:

As linear magnification, $M=4$

Hence, a real magnification ${ m } _{ r }={ m }^{ 2 }$
${ \left( 4 \right)  }^{ 2 }=16$
Surface area of film image on screen $=16\times 100=1600$ ${ cm }^{ 2 }$.

A short linear object of length $b$ lies along the axis of a concave mirror of focal length $f$ at a distance u from the pole of the mirror. The size of the image is approximately equal to :

physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. $b\left (\dfrac {u-f}{f}\right )^{\dfrac {1}{2}}$

  2. $b\left (\dfrac {b}{u-f}\right )^{\dfrac {1}{2}}$

  3. $b\left (\dfrac {u-f}{f}\right )$

  4. $b\left (\dfrac {f}{u-f}\right )^2$

Show answer
Correct Option: D
Explanation:

From mirror formula,


$\cfrac { 1 }{ v } +\cfrac { 1 }{ u } =\cfrac { 1 }{ f } \longrightarrow (1)$

Differentiating, we get  


$\Rightarrow -{ \upsilon  }^{ -2 }dv-{ u }^{ -2 }du=0$

or $\left| d\upsilon  \right| =\left| \cfrac { { \upsilon  }^{ 2 } }{ { u }^{ 2 } }  \right| du \ \longrightarrow (2)$         

Here $\left| dv \right| =$size of image,

$\left| du \right| =$size of object $\left( =b \right) $

From the equation $1$, we write

$\cfrac { u }{ v } +1 =\cfrac { u }{ f } $

Squaring both sides, we get

$\cfrac { { \upsilon  }^{ 2 } }{ { v }^{ 2 } } ={ \left( \cfrac { f }{ u-f }  \right)  }^{ 2 }$

Substituting in equation $2$ we get

Size of the image  $dv=b{ \left( \cfrac { f }{ u-f }  \right)  }^{ 2 }$

Magnification for erect and invented image is

physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. $+ve$ and $-ve$ respectively

  2. $-ve$ and $+ve$ respectively

  3. $+ve$

  4. $-ve$

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Correct Option: A
Explanation:

Magnification is the ratio of height of image and object .

And by convention , height of image formed below principal axis is taken negative and above is taken positive.

Hence, for erect image, $m=+ve$ and for inverted image $m=-ve$.

Answer-(A).

A convex lens of 2 D power is joined with a concave mirror of 1 D power. Equivalent power of instrument will be

physics ray optics and optical instruments problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. $-3D$

  2. $+3D$

  3. $-5D$

  4. $+5D$

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Correct Option: B

If image is real and inverted, mangification will be:

physics ray optics and optical instruments problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. two

  2. negative

  3. one

  4. zero

Show answer
Correct Option: B
Explanation:

According to new Cartesian sign convention, image size for erect image is considered positive and that of inverted image is considered negative.

The object being always erect, the object size is always positive.
So, magnification for a real image, being a ratio of image size and object size is considered negative.

The magnification produced by a concave mirror

physics ray optics and optical instruments problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. is always more than one

  2. is always less than one

  3. is always equal to one

  4. may be less than or greater than one

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Correct Option: D
Explanation:

if object distance < f then m>1

else if object distance >f then m<1

The mirror used in automobiles to see the rear field of view is

physics ray optics and optical instruments problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. concave

  2. convex

  3. plane

  4. none of these

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Correct Option: B
Explanation:

Convex mirrors are used in automobiles to see the near field of view as convex mirror has a wider field of view and it has higher magnification.