Tag: reflection of light at curved surfaces

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Questions Related to reflection of light at curved surfaces

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

What is the formula for spherical mirrors for object distance p and image distance q ?

  1. $\dfrac{1}{p}+q=\dfrac{1}{f}$
  2. $\dfrac{1}{p}+\dfrac{1}{q}=\dfrac{1}{f}$
  3. $\dfrac{1}{p}+\dfrac{1}{q}=f$
  4. $p+\dfrac{1}{q}=\dfrac{1}{f}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Mirror formula is given as: 
$ \dfrac{2}{R} = \dfrac{1}{v} + \dfrac{1}{u} $

where, $ R $ is the radius of curvature of the spherical mirror
$u $ is the object distance from the pole
$ v $ is the image distance from the pole

We know,
$ f = \dfrac{R}{2} $

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

$ \therefore $ For object distance $ p $ and image distance $ q $, mirror formula becomes
$ \dfrac{1}{f} = \dfrac{1}{p} + \dfrac{1}{q} $

Hence, the correct answer is OPTION B.
Multiple choice physics reflection of light at curved surfaces the mirror formula derivation of formula for curved mirrors mirror formula and magnification

A plane mirror produces an image that is

  1. Real, inverted and larger than the object.

  2. Real, upright and same size as the object.

  3. Real upright and smaller than the object.

  4. Virtual, upright and the same size of the object.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A plane mirror always forms a virtual, upright image that is the same size as the object, located at the same distance behind the mirror as the object is in front.

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

A point object is placed at a distance $10cm$ and its real image is formed at a distance of $20cm$ from concave mirror. If the object is moved by $0.1cm$ towards the mirror, the image will shift by about

  1. $0.4cm$ away from the mirror
  2. $0.4cm$ towards the mirror
  3. $0.8cm$ away from the mirror
  4. $0.8cm$ towards the mirror
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$We\quad know\quad \dfrac { 1 }{ f } =\dfrac { 1 }{ u } +\dfrac { 1 }{ v } ;\quad \ where\quad f=focal\quad length=?\ u=\quad initial\quad distance=20\quad cm\ v=\quad final\quad distance=10cm\ \dfrac { 1 }{ f } =\dfrac { 1 }{ -20 } +\dfrac { 1 }{ (-10) } \ f=\dfrac { 20 }{ 3 } \quad cm\ Now\quad object\quad moved\quad towards\quad the\quad mirror=0.1\quad cm,so\quad the\quad new\quad value\quad of\quad u=9.9\quad cm\ Again\quad \quad \quad \ \dfrac { 1 }{ f } =\dfrac { 1 }{ { u } _{ 1 } } +\dfrac { 1 }{ { v } _{ 1 } } \ \dfrac { 1 }{ f } -\dfrac { 1 }{ { u } _{ 1 } } =\dfrac { 1 }{ { v } _{ 1 } } \ \dfrac { 1 }{ { v } _{ 1 } } =\quad \dfrac { 3 }{ 20 } -\dfrac { 1 }{ (-9.9) } \ { v } _{ 1 }=20.4\quad cm\ The\quad change\quad in\quad final\quad distance\quad =20.4cm\quad -20\quad cm=0.4\quad cm\ \ v=\dfrac { 9\times 1600 }{ 3600 } =\quad 4cm/s$

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

A plane mirror produces a magnification of

  1. $-1$
  2. $+1$

  3. Zero

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

The magnification produced by a plane mirror is $+1$ implies that the image formed by a plane mirror is virtual$,$

erect and of the same size$,$ as that of object$.$
Hence,
option $(B)$ is correct answer.

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

If two mirrors are inclined at some angle $\theta$. An object is placed between the mirrors and there are 5 images formed for an object, then $\theta$ is may be

  1. $45^o$
  2. $53^o$
  3. $63^o$
  4. $75^o$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number of images formed by two mirrors at an angle $\theta $ is

$\begin{array}{l} n=\dfrac { { 360 } }{ \theta  } -1 \ \because n=5\, \, \left( { given } \right)  \ \therefore 5=\dfrac { { 360 } }{ \theta  } -1 \ \therefore \theta =\dfrac { { 360 } }{ 6 } ={ 60^{ 0 } } \end{array}$
Hence, the angle may be $63^0$.

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