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

A convex mirror used for rear view on an automobile has a radius of curvature of 3.00m. If a bus is located at 5.00m from this mirror, find magnification?

  1. +0.23

  2. -0.23

  3. +0.45

  4. -0.45
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\dfrac{2}{R}=\dfrac{1}{u}+\dfrac{1}{v}$

$\dfrac{2}{3}=\dfrac{1}{-5}+\dfrac{1}{v}$
$\dfrac{1}{v}=0.866 \Rightarrow  v = 1.15$ cm
Magnification 
$=-\dfrac{v}{u}=-\dfrac{1.15}{-5}=0.23$

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

What is known as linear magnification of spherical mirrors?

  1. Ratio of size of image to size of object

  2. Ratio of shape of image to size of object

  3. Ratio of size of image to shape of object

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation


Ratio of size of image to size of object is known as linear magnification of spherical mirrors.

Linear magnification (m) is the ratio of height of image to that of the object.

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

Magnification $(m) =$ ______

  1. $\dfrac {v}{u}$
  2. $\dfrac {u}{v}$
  3. $\dfrac {h _{o}}{h _{i}}$
  4. $\dfrac {h _{i}}{h _{o}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Magnification is ratio of the size of the image $h _i$ to the size of the object $h _o$.

$m=\dfrac{h _i}{h _o} = \dfrac{-v}{u}$ where $u$ is object distance and $v$ is image distance.

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

For magnification in spherical mirrors object height is :

  1. Negative.

  2. Positive.

  3. For real images positive.

  4. For virtual images negative.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Magnification is the increase in the image size produced by spherical mirrors with respect to the object size. It is the ratio of the height of the image to the height of the object. The height of the object is always positive as the object is always above the principal axis. 

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

In case of a real and inverted image, the magnification of a mirror is:

  1. Positive

  2. Negative

  3. Zero

  4. Infinity
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We know,
Magnification(M)$=\dfrac{height  \ of\   image({h} _{i})}{height\   of  \ object({h} _{o})}$
Here,image is inverted so the $height \  of \  image({h} _{i})$will be negative.
Hence, the magnification of a mirror is negative.

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

The expression for the magnification of a spherical mirror in the terms of focal length (f) and the distance of the object from mirror (u) is

  1. $\frac{-f}{u-f}$
  2. $\frac{f}{u+f}$
  3. $\frac{-f}{u+f}$
  4. $\frac{f}{u-f}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Equation of spherical mirror is $\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$ , where v is the image distance.
solving,
Replacing $v$ with $v=mu$ , 
$\dfrac{1}{f} = \dfrac{1}{u}  (1 + \dfrac{1}{m} ) $
 $u = f (\dfrac{1}{m} +1)$ where m = magnification $= \dfrac{v}{u}$
$u =\dfrac{ f}{m} + f$
$m = \dfrac{f }{ (u - f)}$
Multiple choice physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

A short linear object of length $L$ lies on the axis of a spherical mirror of focal length $f$ at a distance $u$ from the mirror. Its image has an axial length $L$ equal to :

  1. $L{ \left[ \cfrac { f }{ \left( u-f \right) } \right] }^{ 1/2 }$
  2. $L{ \left[ \cfrac { u+f }{ \left( f \right) } \right] }^{ 1/2 }$
  3. $L{ \left[ \cfrac { u+f }{ \left( f \right) } \right] }^{ 2 }$
  4. $L{ \left[ \cfrac { f }{ \left( u-f \right) } \right] }^{ 2 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From mirror formula,       $\cfrac { 1 }{ v } +\cfrac { 1 }{ u } =\cfrac { 1 }{ f } $


On differentiating, we get


      $\cfrac { -dv }{ { v }^{ 2 } } -\cfrac { du }{ { u }^{ 2 } } =0\\ \therefore dv=-du{ \left( \cfrac { v }{ u }  \right)  }^{ 2 }\\ as\quad \cfrac { v }{ u } =\cfrac { f }{ u-f } \\ \therefore dv=-du{ \left[ \cfrac { f }{ u-f }  \right]  }^{ 2 }\\ { L }^{ \prime  }=L{ \left[ \cfrac { f }{ u-f }  \right]  }^{ 2 }$

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

If an object is placed at a distance of 20cm from the pole of a concave mirror, the magnification of its real image is 3. If the object is moved away from the mirror by 10cm, then the magnification is -1.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$M= \frac{f}{f-d _0}$ and real image has M negative

$-3= \frac{f}{f-20}$

$-3f+60=f$

$f=15 cm$

$M= \frac{15}{15-30}$

$M= -1$