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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

The radius of curvature of concave mirror is 24 cm and the image is magnified by 1.5 times. The object distance is

  1. 20 cm

  2. 8 cm

  3. 16 cm

  4. 24 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given that, $\displaystyle R=-24$cm
$\displaystyle f=-12cm$ and $\displaystyle m=1.5$
By the lens formula,
$\displaystyle \frac { 1 }{ v } +\frac { 1 }{ u } =\frac { 1 }{ f } $
$\displaystyle \frac { 1 }{ 1.5u } +\frac { 1 }{ u } =-\frac { 1 }{ 12 } $
$\displaystyle \frac { 2.5 }{ 1.5u } =-\frac { 1 }{ 12 } $
or, $\displaystyle u=-20cm$

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

We want a mirror that will make an object look larger. What combination of image and object distances (from the mirror) will accomplish this?

  1. Image Distance $3.0 cm$, Object Distance $3.0 cm$
  2. Image Distance $2.0 cm$, Object Distance $3.0 cm$
  3. Image Distance $3.0 cm$, Object Distance $5.0 cm$
  4. Image Distance $3.0 cm$, Object Distance $2.0 cm$
  5. Image Distance $3.0 cm$, Object Distance $10.0 cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Magnification by a mirror         $m = \dfrac{-v}{u}$


For option D :    $m = \dfrac{- 3.0}{-2.0} = 1.5$             $\implies m>1$
Thus the data given in option D will make a larger image.

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 magnification produced by a mirror is $+\dfrac{1}{3}.$ Then the mirror is a ____________.

  1. Concave mirror

  2. Convex mirror

  3. Plane mirror

  4. plano convex mirror
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The image produced is virtual and erect and also diminished.


Hence, the mirror must be $convex$ mirror. Concave mirror also produces virtual image but it is enlarged.But convex mirror always produces diminished virtual image.

Answer-(B)

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 an experiment to determine the focal length ($f$) of a concave mirror by the $u-v$ method, a student places the object pin A on the principal axis at a distance $x$ from the pole $P$. The student looks at the pin and its inverted image from a distance keeping the eye in line with $PA$. When the student shifts the eye towards left, the image appears to the right of the object pin. Then:

  1. $x< f$
  2. $f< x< 2f$
  3. $x= 2f$
  4. $x> 2f$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the object and the image move in opposite directions, the position of the object should be in between $f$ and $2f$.
So, $f < x < 2f$

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 linear magnification for a spherical mirror is the ratio of the size of the image to the size of the object, and is denoted by m. Then m is equal to (symbols have their usual meanings)

  1. $\dfrac {u}{u-f}$
  2. $\dfrac {u f}{u-f}$
  3. $\dfrac {f}{u+f}$

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

General equation for a spherical mirror says that:
$\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$

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

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

$\dfrac{v}{u}=\dfrac{f}{u+f}=m$ (magnification)

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 concave mirror forms the real image of an object which is magnified 4 times. The objects is moved 3 cm away, the magnification of the image is 3 times. What is the focal length of the mirror?

  1. 3 cm

  2. 4 cm

  3. 12 cm

  4. 36 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
For mirror $u=\frac {f(m-1)}{m}$
In first case, $u=\frac {f(-4-1)}{-4}$
In the second case, $u+3=\frac {f(-3-1)}{-3}$
On solving, we get $f=36 cm$
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 distance between an object and its doubly magnified image by a concave mirror is: [ Assume $f$ = focal length]

  1. $ 3 f/2 $
  2. $2 f/3 $
  3. $3f$

  4. Depends on whether the image is real or virtual.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The magnification is given as,

$m = \dfrac{{ - v}}{u}$

$2 = \dfrac{{ - v}}{u}$

$v =  - 2u$

Ignoring the sign and using mirror formula, we get

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

$\dfrac{1}{{2u}} + \dfrac{1}{u} = \dfrac{1}{f}$

$\dfrac{{1 + 2}}{{2u}} = \dfrac{1}{f}$

$u = \dfrac{{3f}}{2}$

Here, difference between object distance and image distance is also$u$.

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 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-

  1. $1600 sq. cm$
  2. $800 sq. cm$
  3. $400 sq. cm$
  4. $200 sq. cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $=16\times 100=1600$ ${ cm }^{ 2 }$.