Tag: mirror formula and magnification

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Questions Related to mirror formula and magnification

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

The relation between $u, v$ ( u is the object distance and v is the image distance )  and f for mirror is given by:

  1. $\displaystyle f=\frac{uv}{u-v}$
  2. $\displaystyle f=\frac{2u\times v}{u+v}$
  3. $\displaystyle f=\frac{u\times v}{u+v}$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

or $\dfrac{u+v}{uv} = \dfrac{1}{f}$
or $f=\dfrac{uv}{u+v}$

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

A point source of light is kept in front of a convex mirror of radius of curvature $40 cm$. The image is formed at $10 cm$ behind the mirror. Calculate the object distance

  1. 30

  2. 20

  3. 50

  4. 40
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given: For a convex mirror, $R = -40 cm$.
$v = -10 cm$ (image is virtual).
From mirror formula, we have

$\displaystyle \frac {2}{R}=\frac {1}{u}+\frac {1}{v}$

$\displaystyle \frac {1}{u}=\frac {2}{R}-\frac {1}
{v}=\frac {2v-R}{vR}$

$\displaystyle u=\frac {vR}{2v-R}=\frac {(-10cm) \times (-40cm)}{2 \times (-10cm) - (-40cm)}$

$=+20cm$
Thus, object is placed $20 cm$ in front of the mirror.

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

Mirror formula is valid for:

  1. Convex mirror

  2. Concave mirror

  3. Both A and B

  4. For lenses and mirrors
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Mirror formula is:
$\dfrac {1}{v} + \dfrac {1}{u} = \dfrac {1}{f}$
That is; $\dfrac {1}{\text {Object Distance}} + \dfrac {1}{\text {Image Distance}} = \dfrac {1}{\text {Focal length of the mirror}}$
This relationship is applicable for both concave and convex mirrors.
Multiple choice physics reflection of light at curved surfaces the mirror formula derivation of formula for curved mirrors mirror formula and magnification

Mirror formula can also be written as:

  1. $\dfrac {1}{2v} + \dfrac {1}{2u} = \dfrac {1}{2f}$
  2. $\dfrac {1}{v} + \dfrac {1}{u} = \dfrac {2}{R}$
  3. $\dfrac {1}{v} + \dfrac {2}{u} = \dfrac {1}{f}$
  4. $\dfrac {1}{2v} + \dfrac {4}{u} = \dfrac {3}{R}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Focal length, $f = \dfrac {R}{2}$, where $R$ = radius of curvature

So, $\dfrac {1}{v} + \dfrac {1}{u} = \dfrac {1}{f}$ can be written as
$\Rightarrow \dfrac {1}{v} + \dfrac {1}{u} = \dfrac {2}{R}$

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

Mark the incorrect statement regarding mirror formula.

  1. Values of known and unknown parameters can be used with their proper signs

  2. Sign of unknown parameter comes of its own after calculation

  3. Mirror formula is applicable for both concave and convex mirrors

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

The values of known parameter should be used with their proper sign convention. No sign should be attached to the unknown parameter during calculation. Its sign will come of its own after calculation.

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

The relation among u, v and f for a mirror is

  1. $f = uv/(u+v)$
  2. $v = fu/(u+f)$
  3. $u = fv/(f+v)$

  4. All of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to mirror equation.

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

Similarly,
$v = \cfrac{fu}{u-f}$
$u = \cfrac{fv}{v-f}$

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

The relation among $u,v$ and $f$ for a mirror is:

  1. $f=uv(u+v)$
  2. $v=fu(u+f)$
  3. $u=fv(f+v)$

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

from mirror formula

              $\dfrac { 1 }{ v } +\dfrac { 1 }{ u } =\dfrac { 1 }{ f } $
              $\Rightarrow \quad \boxed { f=\dfrac { uv }{ u+v }  } $
and
          $1+\dfrac { v }{ u } =\dfrac { v }{ f } \Rightarrow \boxed { u=\dfrac { fv }{ f-v }  } $

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

An object is placed at a distance of 1.5 m from a screen and a convex lens is interposed between them. The magnification produced is 4. The focal length of the lens is then

  1. 1 m

  2. 0.5 m

  3. 0.24 m

  4. 2 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Here, $m =\dfrac{v}{u} =-4$

$\Rightarrow u = \dfrac{-v}{4}$------------(1)

Also, $|u| + |v| = 1.5$

$\dfrac{v}{4} + v = 1.5$

$\Rightarrow \dfrac{(v+4 v)}{4} = 1.5$

 $\Rightarrow  v = 1.2 m$

So, putting the value of $v$ in equation (1):
 $u= \dfrac{-1.2}{4} = -0.3 m\,\,\,$

$\therefore  f =\dfrac{uv}{u-v}$

$\Rightarrow f=\dfrac{(-0.3 \times 1.2)}{(-0.3 - 1.2)} = 0.24m$
Hence the correct option is $(C)$

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 
$=-\dfrac{v}{u}=-\dfrac{1.15}{-5}=0.23$